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A MANUAL 





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COPyRICHT DEPOSIT 



A MANUAL OF 
MECHANICAL DRAWING 

SECOND EDITION, REVISED 
By PHILIP D. JOHNSTON 

SUPERINTENDENT AND MECHANICAL ENGINEER 
WEST POINT FOUNDRY 



DAVID WILLIAMS COMPANY, Publishers 

14-16 Park Place, New York 

1907 



VuBRARYofCOHSRESS 
I TW9 Cooles Received 

I APR 13 »907 

rf-Copyrieht Entry 

COPY B. 






Copyright, 1903, ^9°7 
David Williams Company 



INTRODUCTION. 



The lessons embodied in this work are the out- 
growth of some experience in teaching Mechanical 
Drawing, also of many years of practice as a draughts- 
man. 

It is the belief of the writer of this work that a pupil- 
who has mastered the several lessons in their regular 
order will be able to read any drawing, and further, 
that he will be capable of making the usual run of 
drawings that come up in the repair shop, and, in fact, 
in many of the larger works. It is not the object of the 
writer to train designers. That would be out of the 
question, as designing calls for a wide range of knowl- 
edge based upon experience, whereas drawing is 
purely mechanical, and based upon certain unvarying 
laws. 

Some draughtsmen will turn out better work than 
others. This comes partly from practice, and is in 
many cases due to a natural aptitude in the manipula- 
tion of the instruments. 

The pupil in following the work laid out in these 
pages must not content himself with merely copying 
the seveial plates, but should, on the contrary, do each 
one over and over, until he knozvs it absolutely, and can 
see the object of the lesson and understand why each 
line is drawn. He should study the Problems until he 



has them at his finger tips. In working them over and 
over again he is not only learning the problems, but is 
at the same time acquiring facility in the handling of 
the tools. 

The first lesson on the Planes of Projection is of 
first importance, and must be understood, as it is the 
key to all that follows. This cannot be too strongly 
emphasized. 

If any one takes up this book with the idea of merely 
copying the plates, he had better not begin ; there is no 
royal road to acquiring the knowledge necessary to be- 
come a draughtsman. It can be done only by thor- 
oughly understanding the principles underlying the art 
of drawing. The only merit claimed for this work is 
in the selection of the lessons, their systematic arrange- 
ment, and in making the explanations simple and direct 
— stripping them of all needless words. 

The same laws apply to all branches of technical 
drawing ; therefore the pupil who has learned the laws 
upon which technical drawing is based can take up any 
special line, such as mechanical, architectural, etc. 

The aim of this book is to teach these laws and how 
to apply them, anrl as the writer has proved the method 
embodied herein, he feels encouraged to offer the work 
to those who are wanting this knowledge. 



A MANUAL OF MECHANICAL DRAWING. 



CHAPTER I. 



Geometrical Definitions. 



1 Space has three Dimensions, called Length, 
Breadth and Thickness. 

2 A Point has position, but not magnitude. 

3 A Line has length, but neither breadth nor 
thickness. 

4 A Snrface has tzvo dimensions, length and 
breadth. 

5 A Solid has three dimensions, length, breadth 
and thickness. 

6 A Straight line is one which 
does not change its direction at any 
point. 

7 A Curved line is one which 
does change its direction at every 
point. 

8 A Broken line is made up of 
straight lines, each one lying in a 
different direction. 

9 A Plane Surface, or a Plane, is a surface in which, 
if any two points be taken, the straight line joining 
these points will lie wholly within the surface. 

10 A Curved Surface is a surface no part of which is 
plane. 



11 A Plane Figure is a portion of a plane bounded 
by lines either straight or curved. 

12 A Straight Line is the shortest distance between 
two points. 

13 An Angle is the amount of divergence of two 
lines ; the point in which the lines meet is called the 
vertex. 

14 The magnitude of an angle depends wholly upon 
the extent of opening of its sides, and is expressed in 
degrees (°), minutes (') and seconds ("). 

15 Adjacent angles are angles 
that have a common vertex and a 
common side. Thus the angles 
ABC and C B D are adjacent '^- 
angles. 

16 A Right Angle is an angle in- 
cluded between two straight lines 
which meet each other so that the 
two adjacent angles formed by pro- 
ducing, one of the lines through the b ~ 
vertex are equal. Thus if the straight 

line A B meet the straight line C D, making the ad- 
jacent angles ABC and A B D equal to each other, 
they will each be a right angle. 



A MANUAL OF MECHANICAL DRAWING. 



17 Perpendicular lines are lines which make a right 
angle with each other. 

18 An Acute Angle is less than a 
riglit angle. 

19 An Obtuse Angle is greater than 
a right angle. 

20 The Complement of an angle is 
the clifiference between a right angle 
and the given angle. Thus A B D is 
the complement of D B C. c 

21 The Supplement of an angle is 
the difference between two right 
angles and the given angle. Tlius 
A B D is the supplement of D B C. 

22 As before stated (14), the magnitude of an angle 
is expressed in degrees, minutes and seconds. The 
sum of all the angles that can be formed about a given 
point is equal to 360°, and as but four right angles can 
be formed about a given point, it follows that each 
right angle is equal to 90°. 

23 A Triangle is a portion of a plane bounded by 
three straight lines. 

24 A Scalene triangle is one which 
has no two sides equal. 




25 An Isosceles triangle is one 
which has two sides equal. 

26 An Equilateral triangle is' one which 
has all three sides equal. 

27 A Right triangle has one of its 
angles a right angle. The side opposite 
the right angle is called the hypoth- 
enuse. 

28 An Obtuse triangle has one of its 
angles an obtuse angle. 

29 An Acute triangle is one which has 
all of its angles acute. 

30 An Equiangular triangle is one which has all of 
its angles equal ; it is also equilateral. 

31 The Base of a triangle is the side upon which it is 
supposed to stand, and the angle opposite the base is 
called the Vertical angle, and its vertex is called the 
Vertex of the triangle. 

32 Tlic Altiludc of a triangle is the 
perpendicular distance from the base to 
the vertex. 

33 A Quadrilateral is a plane figure bounded by four 
straight lines. 




A MANUAL OF MECHANICAL DRAWING. 



34 A Trapezium is a quadrilateral 
which has no two sides parallel. 




35 A Trapezoid is a quadrilateral 
which has two sides parallel. 

36 A Parallelogram is a quadri- 
lateral which has its opposite sides / 
parallel. 



Z_ 



37 A Rectangle is a parallelogram in 
which all the angles are right angles. 

38 A Square is a parallelogram in which 
all the angles are right angles and all the 
sides equal. 

39 A Rhombus is a parallelogram 
which has its sides equal but its angles 
oblique. 

40 A Rhomboid is a parallelogram , 
which has its opposite sides equal and / 
its angles oblique. ^ — 



41 A Diagonal of a quadrilateral 
is a straight line joining any two oppo- 
site angles. 





42 A Polygon is a plane figure bounded by straight 
lines. 

43 A Diagonal of a polygon is a 
straight line joining the vertices of two 
angles not adjacent. 

44 An Equilateral polygon is one in which all the 
sides are equal. 

45 An Equiangular polygon is one in which all the 
angles are equal. 

46 Polygons are named from the number of their 
sides. A polygon of three sides is a Triangle, one of 
four sides a Quadrilateral, one of five sides a Pentagon, 
one of six sides a Hexagon, one of seven sides a 
Heptagon, one of eight sides an Octagon, one of nine 
sides a Nonagon, one of ten sides a Decagon, one of 
eleven sides an Undecagon, and one of twelve sides a 
Dodecagon. 

47 A Circle is a plain figure bounded 
by a curved line called the Circumference, 
all points of which are equally distant from 
a point within called the Centre. 

48 A Radius of a circle is a straight line 
drawn from the centre to the circumfer- 
ence. 



A MANUAL OF MECHANICAL DRAWING. 



49 A Diameter of a circle is any straight 
line passing through the centre and having 
its extremities in the circumference. 



50 An Arc oi a circle is any portion of 
the circumference. 



51 A Chord of a circle is any straight 
line having its extremities in the circum- 
ference. 



52 A Segment of a cirde is a portion of 
the surface enclosed by an arc and its 
chord. 



53 A Semicircle is a segment equal to 
half the circle. 








54 A Sector of a circle is a portion of a 
circle enclosed by two radii and the arc 
which they intersect. 




55 A Tangent is a straight line 
which touches the circumference but 
does not intersect it. The point where 
the tangent touches the circle is called 
the Point of Tangency. 

56 Two Circumferences are tangent to each other 
when they are tangent to a straight line at the same 
point. 

57 A Secant is a straight line which intersects the 
circumference in two points. 

58 A Polygon is inscribed in a circle when all of its 
sides are chords of the circle. 

59 A Polygon is circumscribed about a circle when 
all of its sides are tangent to the circle, and a circle is 
circumscribed about a polygon when the circumference 
passes through all the vertices of the polygon. 



A MANUAL OF MECHANICAL DRAWING. 



CHAPTER II. 



Problems. 




* 



1 To bisect a straight line, 
draw a radial line to an arc or to 
bisect an arc. Let A B be the 
given line or arc. With A and B 
as centres and a radius greater 
than half the length of the line or 
arc, sweep the arcs intersecting 
at C and D, draw the line C D. 

2 To draw a perpendicular to 
a straight line from a given point 
in that line. Let C be the given 
point in the line A B. With C as 
a centre, draw the arcs at A and 
B, making A C and C B equal ; 

then with A and B for centres, and radius greater than 
A C, draw the intersecting arcs at D. Join C and D. 

3 From the end of a straight ^-^ 
line to draw a perpendicular to 
that line. From some point 
without the line as C, draw the 
arc DAE, passing through A at 
the extremity of the line and cut- 
ting the line at E. From E draw E D through C, 
draw D A, which will be the required perpendicular. 




4 To draw a perpendicular to a straight line from 
any point without that line. Let 
A be the given point ; with A as 
centre draw an arc cutting 
the given line at B and C ; with 
B and C for centres and radius 
greater than B E draw the inter- 
secting arcs at D. Draw A E 
with A and D as points. 

5 To divide a straight line 
into any number of equal parts. 
Let A B be the given line. 
Draw A C at any convenient 
angle (acute) with A B and 

mark A C off into the required number of equal points, 
as I — 2 — 3- Draw C B and parallel with it 3 — 3', 
2 — 2' and I — i'. 

6 To lay off angles of 30° and 
60°. Draw A B and with radius 
A B draw arc B C. With B for 
centre and same radius draw arc 
at C, draw C D perpendicular to 
A B. Then will angle C A D be 
60° and D C A 30°. 





A MANUAL OF MECHANICAL DRAWING. 




:k 



7 To lay off an angle of 45°. 
Draw A C perpendicular to A B, 
with A for centre and radius A B 
draw arcs B and C, draw B C. 
Then will angles A C B and C B A 
be angles of 45°. 

8 To bisect an angle. Let 
it be required to bisect an- 
gle B A C. With A for centre 
and any convenient radius draw- 
arc B C, then with B and C as 
centres and radius greater than half B C draw inter- 
secting arcs at D. Join D A. 

9 Through two given points to 
draw an arc of circle with a given 
radius. Let A and B be the given 
points ; then with radius equal to the 
given radius draw intersecting arcs 
at C. C will be the centre from which to draw the re- 
quired arc. 

10 To find the centre of a circle 
or of an arc of a circle. Take 
any three points in the circum- 
ference well separated as A, B 
and C. With these points as centres 
draw the intersecting arcs, and 
through these intersections draw 
straight lines intersecting at D. D 
will be the required centre. 





11 To draw a circle through three given points use 
the same construction as used for No. 10, the centre D 
being found by the same method. 

12 To draw an arc of a 
circle through three given 
points when the centre is not 
available. Let it be required 
to draw an arc of a circle 
through points A, B and C. 
With A and C for centres 
and radius A C draw the indefinite arcs A F and C G. 
Draw straight lines ABE and C B D. Divide the 
arcs A D and C E into any number of equal parts and 
space off D F and E G with the same divisions. Draw 
Ai', A2', A3', etc., and Ci, C2, C3, etc., the inter- 
sections of these lines will be the points in the required 
arc. 



13 To draw a tangent to a circle 
from a given point in the circumfer- 
ence. Let B be the given point. 
From the centre of the circle draw 
the radius A B and prolong it to C, 
making B C equal to A B. With 
A and C as centres draw arcs in- 
tersecting at D and E ; draw D E, 
which is the required tangent. 




8 



A MANUAL OF MECHANICAL DRAWING. 




>iE 



14. To draw tangents to a 
circle from a point without 
the circle. Let E be the given 
point. Join D and E and on 
D E as a diameter draw the 
circumference intersecting the 
given circumference at F and G, draw E F and E G 
which will be the required tangents. 

15 To describe a circle about a tri- 
angle. Bisect any two sides of the tri- 
angle as A B at D and B C at E and 
erect perpendiculars, and at tlieir 
point of intersection O will be the 
centre of the circle. 

16 To inscribe a circle in a 
triangle. Draw A O bisecting 
the angle A and C O bisecting 
the angle C. With their point 
of intersection O as centre and * 
radius O E draw the required circle. 

17 To describe a circle about a square. Draw 
diagonals A D and B C. Their intersection O will 
be the centre of the circle. 



18. To inscribe a square in a circle. 
Draw diameters A D and B C perpen- 
dicular to each other. Draw A B, 
B D, D C and C A. 






19 To inscribe a circle in a square. 
Draw diagonals A D and B C, with their 
intersection O for centre and O E for 
radius draw the required circle. 

20 To describe a square about a circle. 
Draw diameters A B and C D perpen- 
dicular to each other, with A, B, C and 
D as centres and A O for radius, draw 
arcs cutting each other at E, F, G and 
H. Draw E F, F G, G H and H E. 

21 To inscribe a pentagon in a 
circle. Draw diameters A C and 
B D cutting at O, bisect A O at E 
and from E with radius E B cut A 
C at F. From B with radius B F 
cut circumference at G and with 
same radius step off I, K and H. 
Draw B G, G I, I K, K H and H B. 

22 To construct a pentagon on 
a given straight line. Let A B 
be the given straight line. From 
B erect a perpendicular B C equal 
to half the length of A B. Draw 
A D through C. Make C D equal 
to B C, then B D is the radius 
of the circle circumscribing the pen- 
tagon. From A and B as centres and radius 





B D 



A MANUAL OF MECHANICAL DRAWING. 




describe arcs cutting at O, which is the centre of the 
circle. Step off A B around tlie circumference and 
draw straight Hnes connecting the points. 

23 To construct a hexagon on 
a given straight Hne. Let A B 
be the given line or length 
of side of hexagon. With A 
and B for centres and A B as 
radius draw arcs cutting at 
O. From O with radius O A 
draw circle ABC, and with same 

radius step off points around the circumference ; con- 
nect these points to complete the hexagon. 

24 To inscribe a hexagon in a 
circle. Draw diameter A B and with 
radius equal to the radius of the circle 
step off points around the circum- 
ference ; connect these points with 
straight lines to complete the hexagon. 

25 To describe an octagon on a 
given line. Let A B be the given 
line. Draw A i and B 4 ; also 
draw A G and B H perpendicular 
to A B. From A and B with 

radius A B draw arcs i — 2, 3 — 4, (-— — ^^i Y~ — ^ 

bisect angles G A i and H B 4 

and draw A C and B D. With C and D as centres and 




^ 



'CN 



7t 




radius A B draw arcs E and F, and draw C E and D F 
parallel to A G and B H. With E and F as centres 
and radius A B draw arcs cutting A G and B II. 
Draw E G, F H and G H. 

26 To describe a polygon of any 
number of sides on a given straight 
line. Let A B be the given straight 
line, produce A B and with radius a< 
A B draw a semi-circle, divide this 
semi-circle into as many equal * ^ 
parts as the polygon is to have sides. 

Draw line from A through the divisions D, b and c. 
omitting one point a. With D and B for centres and 
radius A B cut A b at E and A c at F. Draw D E, 
E F and B F. 

27 To inscribe a polygon of any 
number of sides within a circle. 
Draw A B through centre E, draw 
E C perpendicular to A B cut- 
ting circumference at F. Divide E F 
into four equal parts and point off 
tliree of these points from F to C. 
Diyide the diameter A B into as 
many equal parts as polygon is to 
have sides, and from C draw C D through the second 
point cutting the circle at D. Then A D is equal to one 
side of the polygon. Step around the circumference of 
the circle with the length A D to complete the polygon. 




10 



A MANUAL OF MECHANICAL DRAWING, 



CHAPTER III. 
Drawing Instruments, How to Select, Care for and Use Them. 



How to Select Instruments. — The metals usually 
used for drawing instruments are German silver of 
varying quality and steel or iron. Iron is used only 
in the cheapest instruments, and therefore merits no 
further attention. 

The steel should be of the best quality, and properly 
tempered. The cheaper grades of instruments are 
made from castings of German silver, and because of 
the softness of the metal the instruments must be mSde 
bulky and heavy, in order to secure the requisite stiff- 
ness. The makers resort to hammering and swaging 
to overcome this objection, but the remedy is only 
partial, and as a consequence the cheap instruments are 
always clumsy and of poor finish, with badly fitted 
joints, which soon become loose, rendering the instru- 
ment — a compass or dividers, for instance — useless. 
The points are rarely tem.pered, and the soft metal is 
easily bent and always dull. In the best instruments 
the German silver parts are made from hard rolled 
sheet stock, the blanks being first cut by sawing, and 
are gradually reduced to form by milling and filing. 
The joints are carefully fitted, and the hard metal will 
withstand constant use for many years. They are of 
graceful form, light in weight and rigid, the finish is 



of the highest order, the high polish derived from the 
buffing wheel being conspicuous by its absence, but in 
its place is found the exquisite finish known as the 
"mathematical instrument finish." 

This finish brings out all the beauty of the metal, 
leaves all corners clean and smooth, but does not hide 
faults in the material or workmanship. 

The most important instruments are Compasses (in- 
cluding Dividers), Ruling Pens and Bows, which are 
described in detail below. 

Compasses. — The most essential part of a pair of 
compasses is the head, which forms the joint. There 
are two kinds of joints — the tongue joint, in which 
the head of one leg has a tongue, generally of steel, 
which moves between two lugs on the other leg, and 
the pivot joint, in which each leg is reduced to half 
thickness at the head. These are embraced by a clamp 
or yoke, which carries a conical pointed screw in 
each side, the points of the screws working in 
sinks in the compass head. The yoke is further 
provided with a handle with which to manipulate the 
tool. 

The head joint should move freely and evenly 
throughout its entire range — not stiff at one point and 



A MANUAL OF MEGHAN ICAl, l)U AW ING. 



loose at another. It should, however, be tight enough 
to hold its adjustment when set. 

Another important feature in the compass is the 
socket joint for the several "points." In the following 




TONGUE JOINT. 



riVOT JOINT. 



illustrations are shown two good forms, the 
long and strong pentagonal shape and the 
round shank with steel feather or tongue. 
The former should fit snugly into a socket 
of the same shape and be held there by a 
set-screw. The latter (the round shank) is 
held by the spring of the socket, while the 




PENTAGONAL SHANK. 



ROUND SHANK WITH 
STEEL FEATHER. 



tongue insures proper alignment ; the absence of the 
set-screw is considered In- some a desirable feature. 

The alignment is readily tested by inserting the 
several parts and then bending them, as shown by 



the cut, when their points should meet. This is also 
agood test for the alignment of the shank in the socket, 
and every good instrument should stand the test. 

The compass with fixed needle point and interchange- 
able pen and pencil points and lengthening bar is prob- 
ably the most convenient instrument, as the steel points 
are only of use when the compasses are employed as 
dividers, which is very seldom, as every draughtsman 
should have in his set of tools a hairspring divider. 

To sum up, compasses should be of good material 
of proper hardness and of sufficient weight to insure 




COMPASS IN POSITION FOR TESTING ALIGNMENT. 

rigidity in all positions. All joints should move in one 
plane ; the shanks of the several "points" should be 
properly fitted, and the workmanship should be perfect 
throughout. The finish should be put on with care, and 
the instruments should not have a glossy polish, as this 
is only a substitute for the proper finish, and is resorted 
to for the purpose of hiding defects and because it is 
cheap. 



A MANUAL OF MECHANICAL DRAWING, 



The Drawing Pen is the instrument of a Draughts- 
man's outfit which is in nearly constant use, and in 
which defects would therefore become obvious most 
readily. 

Drawing pens are of two different constructions, one 
kind with a hinge joint to allow the blades to be thrown 
apart for cleaning, and the other v/ithout a joint. The 



PEN WITH JOINT. 

joint should, of course, be very carefully made, other- 
wise the upper blade soon becomes shaky, and the pen 
consequently useless. Probably the best pen is the one 
shown in the cut below, in which the upper blade 
springs open when the screw is released from the lower 
blade. A good pen without a joint is to be preferred 
to the one with a joint, no matter how well it is made, 
and it costs less. 



with the drawing paper. The points should be so 
shaped that they are fine enough to admit of absolute 
control of the contact of the pen in starting and ending 
lines, but otherwise as broad and rounded as possible, 
in order to hold a good quantity of ink without drop- 
ping it. The lower blade should be sufficiently firm, to 
prevent the approach of the blades of the pen when 
using it against a straight edge. The spring of the 
pen which separates the two blades should be strong 
enough to hold the upper blade in its position, but not 
so strong as to prevent easy adjustment by the thumb- 
screw. The thread of the thumbscrew should be deeply 
and evenly cut, so as not to strip easily. 

Spring Bows were originally in the shape of small 
compasses, but have been gradually developed into the 
form shown in cut below. What is said in the descrip- 
tion of ruling pens about the necessity for a sufficiently 
stiff spring, and about the relation between spring pres- 
sure and thumbscrew, applies to bows of spring steel, 
just as vi^ell as to blades of ruling pens. 




A good drawing pen should be made of properly 
tempered steel, neither too soft nor hardened to brittle- 
ness. The nibs should be accurately set, both of the 
same length, and both equally firm when in contact 




CARE OF INSTRUMENTS. 



Pens. — Keep a piece of soft cotton or muslin at hand 
and frequently wipe the pen, particularly between the 



A MANUAL OF MECHANICAL DRAWING. 



13 



blades, removing all ink scales that may be clinging to 
them, and always clean the pen thoroughly before lay- 
ing it away after using. Tlie blades being exposed to 
the moisture of the ink will in time become corroded. 
Careful cleaning is the best way to prevent it. 

Never use ordinary writing inks. They contain acids 
which will soon destroy the pen points. When pen 
points become dull it is always best to have them put in 
order by a dealer; the cost is trifling, and the work will 
be properly done, whereas the beginner is liable to do 
more harm than good. Should there be no dealer ac- 
cessible, the draughtsman must of course do his own 
sharpening, practicing on a pen of little value until lie 
has acquired the knack. A good method is as follows : 
By means of the thumbscrew bring the points to- 
gether and round them smoothly and evenly on a fine 
oilstone, a small /Arkansas slip being the best for this 
purpose. This will leave the points thick, but properly 
rounded and of equal length. Now separate the blades 
about an eighth of an inch, take the pen in the left hand 
between the thumb and fore finger and the oilstone in 
the right hand. Bring the pen and stone together, hold- 
ing the pen at a very acute angle to the surface of the 
stone to avoid making the points too short ; hold the left 
hand still and rub the stone against the pen, all the time 
rolling the pen back and forth between the thumb and 
finger until both points are brought to a thin, smooth 
edge. Be careful not to get one blade shorter than the 
other, and never hone the inside of the blade unless it 



is so badly corroded that a smooth point cannot be se- 
cured otherwise. As the work progresses, the pen 
should be occasionally tried with ink until it will make 
a fine, clear line without scratching or cutting into the 
paper. A little practice will enable the average 
draughtsman to do this work with ease and certainty. 

Dividers and Compasses. — Be careful of the points. 
Do not use them on metal ; they are not intended for 
such use. When the points become dull they can easily 
be put into proper shape with the oilstone after the 
manner of pointing a pen.' The needle points should 
be kept sharp, and when they become dull they may be 
repointed on the oilstone. If a lathe with a small 
chuck is available, catch the needle point in the chuck, 
and while it is revolving rapidly sharpen it with the oil- 
stone, using it after the manner of a file. The Arkansas 
stone being very hard and fine, will retain its square 
corners indefinitely, if used only for this purpose. 

The joints of theCompassandDividersshould work 
freely, with just enough friction to hold them in ])o- 
sition when the legs are well opened. If they are too 
tight it is difficult to adjust them accurately to a re- 
quired position. The head joint is readily adjusted by 
means of a key, which is included with the fittings of 
the instrument, but a real good tool will not require 
adjustment even after many years of constant use. A 
cheap one will require very frequent setting. Do not 
oil the joints. 

Bows. — What has been said with reference to pens 



H 



A MANUAL OF MECHANICAL DRAWING. 



applies equally well to bow pens, and but little further 
can be said in regard to them except that the adjusting 
nut and screw should occasionally be oiled and then 
wiped, so that the fingers and consequently the draw- 
ing do not become soiled. 

Do not get into the habit of tossing the instruments 
into a box or drawer ; there is always danger of break- 
ing or bending their points. If you do not have a 
case with compartments to fit the various instruments, 
get a piece of chamois leather and roll the tools iii it, 
keeping the pieces separate as you roll them. 

The T square and triangles, also the scale, should be 
properly protected, otherwise their edges will become 
nicked, and consequently useless. 

It is well to bear in mind that the draughtsman who 
is careless of his tools is very apt to be careless in his 
work. 

TTse of the Various Tools. — The large Compass is for 
drawing circles of say from i-| inches diameter up to 
their limit, which, with the six-inch size, and using the 
lengthening bar, will be about 20 inches diameter. 

The Hair Spring Dividers are used for dividing lines 
and circles, and these, by means of the hair spring, are 
capable of very accurate adjustment. 

The small Bow Pen and Pencil are for small circles, 
l^ inches diameter and under; also for drawing fillets, 
rounding corners, etc., while the small spacing or spring 
divider is used for minute subdivisions for which the 
large hair spring divider would be unhandy because of 



its size. The drawing pen is for straight or curved 
lines, where it is guided by the T square, triangle or 
curve. This pen is adjusted by means of the thumb- 
screw to draw fine or coarse lines at will, and in use 
should be held vertical, or nearly so, that the point, and 
not the side of the pen, is in contact with the paper, and 
it should be pressed firmly but lightly against the guid- 
ing edge, otherwise the line drawn will not be true and 
clean. 

When using the Compass, always have the needle 
point in place ; thus you will avoid boring large, un- 
sightly holes in the paper and the inaccuracies that 
would naturally result therefrom. 

The T square head should be placed against 
the left hand end of the drawing board, and should be 
used only for drawing horizontal lines, while the tri- 
angles are for angles of 30°-6o° and 90°, and 45°. and 
90° to these horizontal lines, the blade of the T square 
being the guide for the triangles. The T square is 
manipulated by the left hand, the triangles being 
moved by the right hand to position and held by the left 
hand while the line is drawn, the blade of the T square 
being held by the left fore arm or wrist. The 30°-6o° 
triangle can also be used for drawing hexagon bolt 
heads and nuts, for dividing a circle into six or twelve 
equal parts, while the 45° triangle will serve for square 
bolt heads or nuts and for dividing a circle into four or 
eight equal parts. See Figs, i and 2. 

They can also be used for drawing parallel lines at 



A MANUAL OF MECHANICAL DRAWING. 



Other angles than those given. Place the two triangles 
together, as in Fig. 3, and bring one edge of one of 
them to the line to which the parallel is to be drawn. 







Fig. I. 



Fig. 2. 



Hold triangle A firmly with the left hand and slide 
triangle B along in either direftion, holding it firmly 
against A, to the point through which the line is to be 
drawn. ,^ 

The Pencil should be sharp- 
ened at both ends, the lead 
quite long, and brought to a 
fine round point at one end and 
to a chisel point at the other. 
The round point is for mark- 
ing oflf from the scale, the 
other for drawing the lines. The reason for sharpen- 
ing one lead fiat is that it will wear longer than a 
round point, but it is not suited for laying off from 
the scale, hence the round point for that purpose. A 




fine file or piece of fine sand or emery paper is used 
for sharpening the lead, preferably the former. Lines 
should be drawn firm and clear, but not too hard, as 
it is difficult to erase them when they are cut deep 
into the paper through too great pressure on the 
hard lead. For compass points and bow pencil use 
Faber's 6H artists' leads, and sharpen them to the 
chisel point as described above. 

To mount a sheet of paper on the drawing board 
proceed as follows : 

In Fig. 4, A is the drawing board, B the pajier. 
First pin the upper left hand corner to the board at C. 

stretch the paper from C 
to the lower right hand 
corner D by drawing the 
palm of the hand in the 
direction of the arrow, 
using enough pressure to 
draw the paper, but not 
sufficient to tear it away 
from C, and put in pin 
D. Ne.xt beginning at 
the middle, stretch the paper toward the lower left hand 
corner and put in pin E, and finally stretch from centre 
and put in the remaining pin D. Except on large 
sheets of paper it is not necessary to use more than the 
four pins at the corners of the sheet. 

The beginner should practice on the figures of Chap- 
ter II until he is thorouehlv familiar with them, at first 



^^ 






A 


y^ B ^\ 




1- 
D 


^^ 


=="- — — = — " ■ 





Fig. 4. 



i6 



A MANUAL OF MECHANICAL DRAWING. 



using the pencil only until he has acquired neatness 
of execution, and not until then should he resort to 
the pens. In fact, he would do well to work at the 
exercises in projection, sections and the construction 
of the various curves and other figures, doing each 
lesson over repeatedly until he is not only familiar with 
them, but can as well make a clean, neat pencil draw- 
ing. Then will be time enough for ink drawing. 

Lines. — The lines usually employed in mechanical 
drawing are : 

The fine full line for the figure to be represented. 

The heavy full line, shade or shadow lines. 

The dot and dash 

for centre lines. 

The dash and two dots ; 

for centre lines. 

The dot * for indicating 

internal parts or parts that may be behind others ; also 
to indicate dimensions. When the dotted line is used 
to mark dimensions the arrow head or witness mark > 
is placed at each end, to indicate the points between 
which the measurement is taken, and the dimension is 
marked on the line in figures thus 

< li'^ > 

In addition to the figures indicating dimensions, there 
are other instructions to be given the mechanic, such as 



directions in regard to finish or machining. When a 
piece of machinery is to be worked or machined in every 
detail, the general direction "Finish all over" tells the 
mechanic it is to be turned, planed, filed, or otherwise 
worked to bring it to the required dimensions. Fur- 
ther, the expression informs the pattern maker or smith 
that additional metal over the dimensions given is to 
be left to be removed in the operation of finishing. 
When only certain surfaces are to be finished, leaving 
the remaining parts rough, the mark "f" is placed upon 
the surface. 

When one piece is to be fitted to another hard or 
tight, such as a bolt into a hole, the kind of fit is 
marked on the particular piece, such as "driving fit," 
which means that the bolt is to be turned of such a size 
that it must be driven to place with a hammer. Again, 
"reamed fit" would mean that the bolt should be turned 
so that it can be pushed or lightly tapped to place, and 
yet must fit so perfectly that it will not admit of the 
slightest movement. 

Any special directions can be given, but they should 
be stated concisely. When the directions cannot be 
marked directly upon the object, an arrow connecting 
the explanation with the point or part referred to nuist 
be used. Examples of these directions are given in 
the several lessons on shop drawings. 

In drawing these broken lines, acquire the habit of 
making all the dots equal in length ; also the spaces 
between them. 



A MANUAL OF MECHANICAL DRAWING. 



17 



Where it is desired to show only a portion of an ob- 
ject it is represented as broken. If the object is square 
or rectangular in section the 
break is represented bv 



J 



a ragged line, thus : 
If round, thus : 



7 



Shade lines, while not necessary, always improve the 
appearance of the drawing, making it stand out from 
the paper, and aiding the eye in taking in the form. 
The rule to be followed in putting them in a drawing is 
simple. The light is supposed to strike the upper and 
left hand sides of the object — that is, to strike at an 
angle of 45°, thus putting the right hand side and bot- 
tom in shadow, or rather making them cast a shadow. 
This is shown in the figure of a 
square (Fig. 5), the arrow indicat- 
ing the direction of the light rays. 
Objects having corners or edges are 
plainly shown by means of these 
shade lines. A cylinder in ele- 
vation should not be shaded, but the 
Fig. 5. square end should be shaded, as in 

Fig. 6. A cylinder in 
plan would show a circle, 
and this should be shaded, 
the shade line extending 
around half the circum- 
ference, the heaviest part 




Fig. 7. 



Fig. 6. 



of the line being opposite the highest light and grad- 
ually reducing in width to that 
of the light line. To do this, 
draw first the line representing 
the cylinder, then find a new 
centre in a line following the 
direction of the light, and with 
the same radius draw another 
line on the lower right side for 
the outside, and the upper left 
for the inside of the cvlinder. 
In Fig. 7 this is shown with 
lines exaggerated in order to show how the compass 
point is to be placed. 

An object shown in section is indicated bv "section 
lines" — that is, by parallel lines at the angle of 45° to 
the main lines of the object. When the object is made up 
of two or more pieces the section lines for one piece 
are drawn at right angles, or 90°, to those of the next 
piece. See Fig. 8 and the lesson plates. 

Lines are also used to represent the various ma- 
terials of construction when shown in section. These 
are shown on Plate 41. 

The light lines should be uni- 1 
form in breadth, as well as the 
shade lines, while section lines 
should vary according to ma- 
terial to be represented. Many j 
draught.=men do not use the 



ViG. 8. 



i8 



A MANUAL OF MECHANICAL DRAWING. 



"conventional" lines referred to above, but instead em- 
ploy only the simple fine line as in Fig. 8, and indicate 
the material to be used by marking its name upon the 
figure. 

Line Shading is sometimes employed, but not often, 
as when it is considered necessary to make some par- 
ticular piece or part of a drawing conspicuous, or it is 
desired to make a picture of the drawing, as, for in- 
stance, a complete machine. This is accomplished by 
varying the widths or thickness of the lines and the 
spaces between them. Several examples of line shading 
are given in Plate 42. 

Fig. I. End and side elevation of a cylinder. The 
rule to be followed is for the direction of light the 
same as for shade lines. Objects in elevation are 
lighted from the upper left hand corner, therefore the 
highest light would be at the point where the light 
strikes full upon the surface and the darkest point 
about at right angles to the high light. This is clearly 
shown in Fig. i. A hollow object, such as a cylinder 
in section, would show light and shadow just the op- 
posite of what would appear on the outside surface of 
the cylinder. (See Fig. 2.) 

Figs. 3 and 4 show a square and hexagonal prism in 
elevation ; above them the plans. In the case of the 
plan the light will strike from the lower left hand, as 
shown. In this case, the surfaces being flat, the lines 
are equally spaced over the surface. The flat side, re- 
ceiving the light direct, being covered with light lines 



equally spaced, while the side away from the light is 
covered with heavy lines, also equally spaced. In Fig. 
4, there being three sides, each one being lined dif- 
ferently, the lightest side next the light and the darkest 
farthest from the light. In Fig. 5 is shown a flat sur- 
face, and to show the effect of the slightest variation, 
either in the width or spacing of the lines, one of the 
spaces is purposely increased ; this at once makes a 
break in the surface. This shows at once the necessity 
for absolute accuracy in both spacing and thickness of 
the lines. In Fig. 6 is shown a waving or corrugated 
surface, while Fig. 7 shows how a sphere should be 
shaded. The point of high light would be a small circle 
somewhat less in diameter than the radius of the sphere. 

Lettering'. — Plain, strong letters and figures only 
should be used, fancy lettering being out of place on 
a mechanical drawing; they are also liable to be con- 
fusing to the mechanic who is to work from the draw- 
ing. There are two styles that are particularly suited 
to drawings. The Roman for titles and the Italic, with 
figures to correspond, for notes on the body of the 
drawing and for dimensions. The light-faced Roman 
may also be used for this purpose. These several alpha- 
bets are given on Plate 40. 

As to titles, these are gradually being discontinued by 
most of the large workshops, and the simple system of 
numbering substituted therefor. The drawing under 
this system bears in one of its corners a large number 
or letter, which indicates its class, or the group to 



A MANUAL OF MECHANICAL DRAWING. 



19 



which it beloni::s, ami anotlier number the drawer in 
which it is filed ; also in small letters the scale or scales, 
if more than one on the sheet, the date of completion, as 
well as the initials of the draughtsman and the checker. 
If there is more than one sheet to a given machine then 
these sheets should be plainly numbered consecutively. 

An index is kept, which gives the name of the ma- 
chine and the part or parts represented on each sheet, 
as well as the number of the sheet and the drawer in 
which it is kept, so that any particular drawling can be 
found instantly. 

A sample of a form used very generally is given in 
the annexed figure, in which all of the means or marks 
for identification are given. 



Mark .„ 

No. Sheets 
Drawn by 
Traced by 
Scale 


Drawer 

Sheet No. 


Checked by 

Date 


Smith, 


Jones & Co. 



Should the drawing be changed at any subsequent 
time, the changes are noted on the drawing and the 
record of the change is made above the title in the form 
of a sub-title, thus : 



Altered 



Dale ^/o/o:s 



Parts 2y 



Example : It is learned that a certain machine can 
be improved by making a slight change in a i)articular 
casting. Said change is a minor one, and w ill not neces- 
sitate a new drawing. Accordingly, the old drawing 
is changed, and the date and number of the part re- 
corded as above. That is, part No. 27 was altered 
May lOth, 1903. If more than one part is altered these 
changes are duly recorded, one beneath the other, as 
indicated. If the change requires a new drawing, this 
drawing is given a new number, and the fact noted on 
the old drawing, which is preserved, thus making the 
history of the development of the machine complete. 
This follows upon the practice of numbering each in- 
dividual piece of the machine as is indicated on 
Plate 52. 

Some of the large shops simply mark in the lower 
right hand corner of their drawings in large figures and 

letters, as: KjO''/\''0. meaning jMachine No. 36. 

3-27-03 
Drawer A, Sheet No. 5, March 27lh, 1903. All other 
data being recorded in the index book. 

Dimensions. — In putting the figures or dimensions on 
a drawing, do not be afraid of putting on too many. 
The drawing should answer every question the me- 
chanic can ask — in short, should give full information 
upon every point and for every class of mechanic. 
Therefore the draughtsman should consider who will 
work from the drawing: if pattern makers, machinists 



20 



A MANUAL OF MECHANICAL DRAWING. 



and blacksmiths, suppl}' full information for each one. 
In fact, let the drawing be looked upon as something 
to indicate certain forms, and make it supply full in- 
formation from which to reproduce these forms in the 
metals or other materials. Feet are indicated by a 
single mark and inches by two marks, and are sepa- 
rated by a dash. Two feet six and one-half inches 
would be written on the drawing thus, 2' — 6^". Three 
feet and one-quarter of an inch thus, 3' — oj". 

The Scales. — Those usually employed are half size, in 
which a half inch on the drawing repre- 
sents an inch on the machine, then each 
eighth of an inch is equal to a quarter 
of an inch, and each sixteenth to an 
eighth ; quarter size, or three inches to a 
foot ; eighth size, or one and a half inches 
to one foot ; one-twelfth, or one inch to 
one foot; one-sixteenth, or three-quar- 
ters of an inch to the foot ; one 
twentjf-fourth, or half inch to the 
foot, and so on down. Smaller than one-quarter inch to 
the foot is rarely used. The larger the scale the better, 
as it is easier to show detail on a large scale than a 
small one ; also large scale drawings are more likely to 
be accurate. Whatever the unit chosen to represent a 
foot it is divided into twelve equal parts, representing 
inches, and if the unit is large enough these are further 
divided into halves, quarters and even eighths, as in 
the scale of 3" = i foot. 



The beginner should acquire accuracy in drawing the 
lines, as well as in figuring the drawing. Certain main 
dimensions are always required to begin the drawing, 
but when it is completed and the dimensions are to be 
put in, these must be taken from the drawing with the 
scale. When there are a number of intermediate di- 
mensions, be sure that their sum is equal to the extreme 
or over all dimension, as in the sketch for a crank shaft 
(Fig. 9). 

Freehand sketching should be acquired by every 




Fig. 9. 



draughtsman, as he is frequently called upon to make 
sketches from broken pieces of machinery, to be after- 
wards used as notes from which to make drawings. 
These sketches consist of outlines giving the form of 
the object in as many views as may be necessary to 
show its form and bearing the measurements required 
for making a correct drawing. 

In taking a dimension from the scale — for instance 
an inch — do not mark it oiif either full or scant, but let 



A MANUAL OF MECHANICAL DRAWING. 



21 



it be just an inch. Always draw tlie centre line or lines 
about which the figures are to be constructed as the 
starting point, and work from these centre lines. 

Do not consume needless space. Place the several 
views of an object near enough to each other that their 
relation will be established at a glance, and do not make 
needless views. Consider the form and decide what are 
the best points from which to view it, and make the 
drawing accordingly. 

In drawing a tangent to an arc or a circle, make it 
truly tangent ; also in putting in fillets or in rounding 
corners do it thus : \ Not thus : 

Or thus : 

In drawing or finishing a drawing with ink it is best 
to fill in the circles and arcs first, afterwards drawing 
the straight lines, the reason being that it is easier to 
fit a tangent or straight line to an arc or curve than is 
the reverse process. 

INSTRUMENTS REQUIRED. 

The mechanical or architectural draughtsman may do 
his work with comparatively few instruments, there- 
fore there should be no real excuse for his buying any 
but the best quality, and the beginner is urged to bear 
in mind the various descriptions given at the beginning 
of this chapter when making his selection. The fol- 
lowing tools and supplies will be reciuircd. and thoy 



will be found ample in number and size for the average 
of the work done b)- the draughtsman : 

One Compass 5I inches or 6 inches long, with fi.xed 
needle point, pen and pencil points and lengthening bar. 




One Hair Spring Divider, 4 inches long. 




One Set Spring Bows 3! inches long, consisting of 
pen, pencil and spacer. 




2 A MANUAL OF MECHANICAL DRAWING 

One Drawing Pen, 4^ or 5 inches long. 



One Triangular Scale 12 inches long, with divisions 
in twelfths, those coated with white celluloid being the 
best. 'J'-'' 




I 



One Protractor, 4-inch or 5-inch, of German silver, 
graduated to degrees or half degrees, to be used for 
measuring and laying ofif angles. 



One Triangle 7" 45°, of celluloid or rubber. One 
Triangle 9" 30°-6o°, of celluloid or rubber. 





Two or more Irreg- 
ular Curves. Some of 
the many forms of 
these are -shown in cut. 
They should be either 
of celluloid or rubber. 



One Drawing Board, not less than 20x26 inches. 

A fevv" Thumb Tacks, a piece of good Rubber, a 6H 
Pencil, either Hardmuth's or Faber's; a 6H Artist's 
Lead for compass points, and a few sheets of good 
detail drawing paper, about 16x20 inches. 

There are many other instruments which are con- 
venient, but not necessary, such as 2)h "^^h Compasses 



A MANUAL OF MECHANICAL DRAWIXG. 



^Z 



with fixed needle and pen or {>encil points. Tlicsc in 
range come between the large compass and the spring 
bows, and as the jxDints arc fiy ! there is no ciianging 




from pencil to pen. Further, the majority of the arcs 
and circles the drauglitsman deals with come within 
their range. 

Another very useful tool is the Beam Compass, 
which is used for drawing very large circles. It 
takes its name from the fact that the two heads are 




clamped to a wood bar or beam. It is fitted with pen, 
pencil and needle points. 



24 



A MANUAL OF MECHANICAL DRAWING. 



CHAPTER IV. 



Mensuration^ Mechanical Powers and Tables. 



Symbols and abbreviations : 

The sign for equality is = and is read equal to. 

The sign for addition is -f- and is read plus. 

The sign for subtraction is — and is read minus. 

The sign for multiplication is X and is read multi- 
plied by. 

The sign for division is -^- and is read divided by. 

When a number is multiplied by itself several times 
this operation is indicated by writing to the right and 
above it a small figure denoting the number of times 
the multiplication is performed or the number of times 
the number is taken as a factor. Thus 6- indicates 
that 6 is taken twice as a factor and is read six square; 
5* indicates that 5 is taken three times and is read five 
cube; while 7^ means that 7 is taken five times and 
is read seven to the fifth pozver. The factor of which 
a power is composed is called the root, and is indicated 
in the radical sign Vj and the operation of finding 
the factor is called the "extraction of the root." The 
power is written under the radical sign and a small 
figure called the index, or exponent, is written above 

it to indicate the root to be extracted. Thus ^/ 

indicates that the cube root of twenty-seven is to be 



ascertained, ^P^ indicates that the fifth root of two 

hundred and forty-three is to be extracted. When no 
index or exponent is written it is understood that the 

square root is to be extracted thus : ^r^ 

The operation of extracting roots can be learned from 
any arithmetic. 

Diameter is written Diam. Radius is written Rad. 
Circumference is written Circ. Perpendicular is writ- 
ten Perp. The sign tt, called Pi, indicates ratio of 
diameter of circle to circumference. 

The Circle. 

Diam. squared X .7854 = area. 
Diam. X circ. -f- 4 = area. 
Rad. X 2 circ. = area. 
Diam. X 3-i4i6 = circ. 
Circ. X -31831 = diam. 
Circ. -f-- 3.1416 == diam. 
Square root of area X 1.1284 := diam. 
TT = 3.1416. 

Diam. of a sphere X -806 = dimensions of an equal 
. cube. 



A MANUAL OF iMKCllAiN'ICAL DRAWING. 



Diam. of a sphere X .6667 = length of equal cylinder. 
Diam. X .8862 = side of an equal square. 
Side of a square X 1.128 =^ diam. of an equal circle. 
Square of the diam. of a sphere X 3- 1416 = convex 

surface. 
Cube of the diam. of a sphere X -5236 = solidity. 
Sqr. inches X .00695 = square feet. 
Cubic inches X .00058 = cubic feet. 
Cubic feet X -03704 = cubic yards. 




Area 



- Base X \ height h. 
bh 



Area = Side A X side B. 



xA.rea ■{ 



r Divide into two triangles and 



take the sum of their areas. 



Area 



f Divide into two triangles and 
1 take the sum of their areas. 




.\rea -j 
I 



Divide into two triangles and 
take the sum of their areas. 



Perimeter 



7t yj 



D--|-d- (D— d;- 



8.8 



Area = Dd ^ 0.7854 Dd. 




Area = area of D — area of d. 
Area = 0.7854 (D-— d-j. 

Sector. 
Area = ^ 1 r = half length of arc X ratJ- 
or rad. X arc -^ 2. 

Tt I"' E 
Area = — -p — = .008727 r- E. 
360 ' ' 




Segment. 
Area = i [1 r — c (r-h)] or 



;r r= E 

360 



(r-h) 1 

180 1 

Tt r 



TT r E 
^ "iScT 

= 57-2956 



0.0175 r E. 




Cylinder. 
Convex surface = circumference X 
height. Entire surface = area of two ends 
+ convex surface. Volume = area of one 

end X height. 



26 



A MANUAL OF MECHANICAL DRAWING. 




Cone. 
Convex surface = i tt d 1 ^= circumfer- 
ence of base X i slant height. Entire 
surface = area of base + convex sur- 

0.7854 d^ h 

face. Volume = 

3 . 

Sphere. 

Entire surface = 4 ;r r^ or tt d^ or d^ X 

3.1416. Volume = 0.5236 d*. 



Annulus. 
Entire surface = 4 ;r- Rr = 9.8696 Dd. 
Volume ^ 2 TT- Rr= = 2.4674 Dd^ 




Truncated Cone. 

Convex surface = — (D -)- d). 
2 

Entire surface = convex surface + 

area of both ends. Volume - - .26i8h 

(D^ + Dd + d^). 

Convex surface ^= perimeter of base 
X 2 ^- Entire surface = convex sur- 
face + area of base. Area of base, 
divide into triangles and take sum of 
their areas. Volume = 1-3 area of 
base X h- 




Convex surface = J 1 (P + p). Entire 
surface = convex surface + sum of 
areas of upper and lower bases. Volume 

= - (A + a + -./ Aa) ; a = area 
3 ^ 

upper base or surface, A = area lower base or sur- 
face; p = perimeter upper base, P = perimeter of 
lower base. 

The Mechanical Powers. 

The Statistical Law for levers is : The weight multi- 
plied by its distance from the fulcrum is equal to the 
power multiplied by its distance from the fulcrum, or 
PL = Wl, then, 






Wl 
P = ^,W 



PL 



Pa 



Wa 




^ ~ W + P' -^ ~ W + P 



Bent levers are treat- 
ed the same as straight 
levers, as in the figure 
P annexed. 



A MANUAL OF MECHANICAL DRAWING. 



27 



_J^ 

I X a 

© 

W 1 PI W a 

L 1 W — p 



1 = 



Pa 



W 



\h 



4. 



p = 



L ' 



w^¥=.-r^w 



L = 



W 



P-W 

Compound Levers. — When a compound lever is in 
equilibrium, the power multiplied by the continued 
product of the alternate arms commencing with the 
power, is equal to the load multiplied by the continued 
product of the alternate arms commencing with the 
load. f! 

L' V Pi 



T 



TT 



I' X PF X P'F' X P"F"= W X WF" X L'— F'X LF. 




P = 



Wheel and Axle. 
W 1 ... PL Pa 

' \ ' '- W +P' 

Wa 



W 



L = 



W + P' 




Differential Block. 
Power multiplied by radius 
of crank is equal to the load 
multiplied by half the difference 
of tlie radii of the two parts of 
the axle or drum. 



Pulley. — Load is equal to the power multiplied by 
the number of parts of rope supporting the load or 
running block. This law^ applies only when one con- 
tinuous rope passes through the whole system, and 
when its parts are parallel. 

Inclined Plane. 
The power = load X ratio of the 
vertical height of the plane to its 
length. 




P = 



L X side BC. 



Side AC. 



Power = load X ratio of 
vertical height of plane to its 
base. 



L = 



P X side AC. 
Side BC. 




P = 



L X side BC. 
Side AB~ 



P X side AB. 
Sidc~BC7~~ 



28 



A MANUAL OF MECHANICAL DRAWING. 



P = 



The Wedge. — 
L X side BC. 



Side AB. 



L = 



P X side AB. 
Side BC. 



Law. — The power is to the load as the height 
of the wedge is to its base. These laws are of 
no practical value beyond the fact shown: that the 
efficiency of the wedge or its power increases with its 
thinness. The reasons for this are that the power is 



applied not by continnous force but by percussion^ for 
which there are no numerical standards of comparison. 



The Screw. — P = 

pitch of screw, r = 
radius through which 
force acts, W =: weight 
or resistance. 

WP 27rrF 

2 Ttr P 




A MANUAL Of MrCCIIANICAI. DRAWING. 



29 



TABLES. 

















TABLE I. 


























Decimal Parts of an Inch 


FOR Each ^jTH. 












Frac- 








Frac- 








Frac 






Frac- 








tion. 


Ads. 


^ifhs. Decimal. 


t.on. 


■hds. 


^iths. Decimal. 


tion. 


^rfs. ^itlis. Decimal. 


tion. 


Arf«. 


^fths. Decimal. 






I 


015625 






17 


265625 




33 


515625 






49 


765625 




I 


2 


03125 




9 


18 


28125 




17 34 


53125 




25 


50 


78125 






3 


046875 






19 


296875 




35 


546875 






51 


796875 


iV 


2 


4 


0625 


A 


TO 


20 


3125 


9 
1 5 


18 36 


5625 


H 


26 


52 


8125 






5 


078125 






21 


328125 




37 


578125 






53 


828125 




3 


6 


09375 




II 


22 


34375 




19 38 


59375 




27 


54 


84375 






7 


109375 






23 


359375 




39 


609375 






55 


859375 


Vs 


4 


8 


125 


H 


12 


24 


375 


•/8 


20 40 


625 


H 


28 


56 


875 






9 


140625 






25 


390625 




41 


640625 






57 


890625 




5 


10 


15625 




13 


26 


40625 




21 42 


65625 




20 


58 


90625 






II 


171875 






27 


421875 




43 


671875 






59 


92187s 


A 


6 


12 


187s 


■^ 


14 


28 


4375 


1 1 
1 1) 


22 44 


6875 


1 5 


30 


60 


9375 






13 


203125 






29 


453125 




45 


703125 






61 


953125 




7 


14 


21875 




IS 


30 


46875 




23 46 


71875 




31 


62 


96875 






15 


234375 






31 


484375 




47 


734375 






63 


984375 


J4 


8 


16 


25 


V. 


15 


32 


5 


•M 


24 48 


75 


I 


32 


64 I 


000 



30 



A MANUAL OF MECHANICAL DRAWING. 



Inches. 



Vr 



TABLE II.— DECIMAL EQUIVALENTS OF A FOOT FOR EACH jVd OF AN INCH. 

5" 
4167 

4193 
4129 

4245 
4271 
4297 
4323 
4349 
4375 
4401 
4427 
4453 
4479 
4505 
4531 
4557 
4583 
4609 

4635 
4661 
4688 
4714 
4740 
4766 
4792 
4818 

4844 
4870 
4896 
4922 
4948 
4974 
I 

To use the above table : 
Find the decimal equivalent of gf J inches. 

Follow the horizontal line of figures marked fj until it intersec 
.8307. Again, find the fraction for .6380. The quantity .6380 is at 
marked |J, therefore the decimal quantity is equal to 7§J inches. 



V& 



% 



Va 



H 






I 


2 


3 


4 





0833 


1667 


.2500 


3333 


.0026 


0859 


1693 


.2526 


3359 


.0052 


0885 


1719 


■ 2552 


338s 


.0078 


0911 


1745 


.2578 


3411 


.0104 


0937 


1771 


.2604 


3437 


.0130 


0964 


1797 


.2630 


3464 


.0156 


0990 


1823 


.2656 


3490 


.0182 


1016 


1849 


.2682 


3516 


.0208 


1042 


1875 


.2708 


3542 


.0234 


1068 


1901 


.2734 


3568 


.0260 


1094 


1927 


.2760 


3594 


.0286 


1 120 


1953 


.2786 


3620 


.0312 


1146 


1979 


.2812 


3646 


■0339 


1 172 


2005 


.2839 


3672 


• 0365 


1198 


2031 


.2865 


3698 


.0391 


1224 


2057 


.2891 


3724 


.0417 


1250 


2083 


.2917 


37SO 


.0443 


1276 


2109 


• 2943 


2,77€> 


.0469 


1302 


2135 


.2969 


3802 


.0495 


1328 


2l6l 


■ 2995 


3828 


.0521 


1354 


2188 


.3021 


3854 


■ 0547 


1380 


2214 


• 3047 


3880 


• 0573 


1406 


2240 


■ 3073 


3906 


• 0599 


1432 


2266 


• 3099 


3932 


.0625 


1458 


2292 


•3125 


3958 


.06=1 


1484 


2318 


.3151 


3984 


.0677 


1510 


2344 


•3177 


4010 


.0703 


15.36 


2370 


.3203 


4036 


.0729 


1562 


2396 


.3229 


4062 


.0755 


1589 


2422 


• 3255 


4089 


.0781 


1615 


2448 


.3281 


4115 


.0807 


1641 


2474 


•3307 


4141 



6" 


7" 


8" 


9" 


10" 


11" 


5000 


•5833 


6667 


7500 


8333 


9167 


5026 


•5859 


6693 


7526 


8359 


9193 


5052 


.5885 


6719 


7552 


8385 


9219 


5078 


•5911^ 


6745 


7578 


841 1 


9245 


5104 


■5937 


6771 


7604 


8437 


9271 


5130 


■ 5964 


6797 


7630 


8464 


9297 


5156 


■5990 


6823 


7656 


8490 


9323 


5182 


.6016 


6849 


7682 


8516 


9349 


5208 


. 6042 


6875 


7708 


8542 


9375 


5234 


.6068 


6901 


7734 


8568 


9401 


5260 


.6094 


6927 


7760 


8594 


9427 


5286 


.6120 


6953 


7786 


8620 


9453 


5312 


.6146 


6979 


7812 


8646 


9479 


5339 


.6172 


7005 


7839 


8672 


9505 


5365 


.6198 


7031 


7865 


8698 


9531 


5391 


.6224 


7057 


7891 


8724 


9557 


5417 


.62=;o 


7083 


7917 


8750 


9583 


5443 


.6276 


7109 


7943 


8776 


9609 


5469 


.6302 


7133 


7969 


8802 


963s 


5495 


■ 6328 


7161 


7995 


8828 


9661 


5S2I 


.6354 


7188 


8021 


8854 


9688 


5547 


.6380 


7214 


8047. 


8880 


9714 


5573 


.6406 


7240 


8073 


8906 


9740 


5599 


.6432 


7266 


8099 . 


8932 


9766 


562s 


.6458 


7292 


8125 


8958 


9792 


5651 


.6484 


7318 


8151 


8984 


9818 


5677 


.6510 


7344 


8177 


9010 


9844 


5703 


.6536 


7370 


8203 


9036 


9870 


5729 


.6562 


7396 


8229 


9062 


9896 


5755 


.6589 


7422 


8255 


9089 


9922 


5781 


■ 6615 


7448 


8281 


9115 


9948 


5807 


.6641 


7474 


8307 


9141 

r 


9974 
0000 


he vertical column 


headed 9 


'; at the intersection find 


intersection of c6 


umn headed 7" and horizonta 


line 



A MANUAL OF MIXH AN ICAL DRAWING. 



31 













TABLE III. 




















Circumference and Area 


OF Circles. 










Diam- 


Circum- 




Diam- 


C'xrcwn- 




Diam- 


Cirtum- 




Diam- 


Circum- 




eter. 


ference. 


Area. 


eter. 


fercnce. 


Area. 


eter. 


fcrcnce. 


Area. 


eter. 


ference. 


Area. 


^ 


.4900 


.000192 


H 


8.6394 


S-9396 


H 


20.S131 


34-4717 


Az 


32.9868 


86.5903 


A 


.09818 


. 000767 


-A 


9.0321 


6.4918 


H 


21.2058 


35-7848 


Vs 


33.3795 


88.6643 


A 


. 19635 


.003068 


3 


9.4248 


7.0686 


■As 


21.5985 


37.1224 


Va 


33.7722 


90.7628 


% 


•3927 


.012272 


% 


9-8175 


7.6699 


7 


21.9912 


38.4846 


-/8 


34.1649 


92.8858 


A 


.589 


.027612 


H 


0.2102 


8.2958 


Vs 


22.3839 


39-8713 


11 


34.5576 


95-0334 


M 


.7854 


.049087 


Vs 


. 6029 


8.9462 


H 


22 . 7766 


41.2826 


Vs 


34.9503 


97-2055 


A 


■98175 


. 076699 


'A 


0.9956 


9.6211 


H 


23-1693 


42.7184 


K 


35-343 


99.4022 


K 


I.11781 


. 1 10447 


H 


1-3883 


10.3206 


K2 


23-562 


44.1787 


As 


35-7357 


101.6234 


A 


1-37445 


.15033 


Va 


I. 781 


11.0447 


Ai 


23-9547 


45-6636 


Az 


36.1284 


103.8691 


'A 


I . 5708 


■19635 


% 


2.1737 


11-7933 


Ya 


24-3474 


47-1731 


As 


36.5211 


106.1394 


A 


1-76715 


.248505 


4 


2.5664 


12.5664 


Ai 


24.7401 


48.7071 


Va 


36.9138 


108.4343 


•% 


1.9635 


.306796 


''u 


2.9591 


13-3641 


8 


25-1328 


50.2656 


As 


37.3065 


110.7537 


H 


2.15985 


.371224 


'4 


3.3518 


14-1863 


A& 


25-5255 


51.8487 


12 


37.6992 


113.098 


H 


2.3562 


-441787 


V>i 


3-7445 


15 033 


Aa 


25.9182 


53-4563 


Ks 


38.0919 


115.466 


}| 


2-55-^55 


.518487 


A. 


4.1372 


15-9043 


H 


26.3109 


55-0884 


Aa 


38.4846 


117.859 


rs 


2.7489 


.601322 


% 


4-5299 


16.8002 


^^ 


26 . 7036 


56^7451 


Vs 


38.8773 


120.277 


li 


2.94525 


. 690292 


•34 


4.9226 


17.7206 


As 


27-0963 


58.4264 


Az 


39-27 


122.719 


1 


3.1416 


■ 7854 


r& 


5-3153 


18.6655 


34 


27.489 


60.1322 


As 


.39-6627 


125.185 


j^ 


3.5.343 


■99402 


5 


5-708 


19-635 


As . 


27.8817 


61.8625 


Ax 


40.0554 


127.677 


^4 


3-927 


1.2272 


As 


6.1007 


20 . 629 


9 


28.2744 


63.6174 


li 


40.4481 


130.192 


^ 


4-3197 


1.4849 


A 


6.4934 


21.6476 


As 


28.6671 


65-3968 


13 


40.8408 


132.733 


/2 


4.7124 


I. 7671 


Vs 


[6.8861 


22 . 6907 


Aa 


29-0598 


67 . 2008 


Ks 


41-2.335 


135-297 


Vs 


5-1051 


2.0739 


A 


7.2788 


23-7583 


■Ks 


29-4525 


69.0293 


Aa 


41.6262 


137-887 


H 


5 4978 


2.4053 


H 


7.6715 


24-8505 


>2 


29-8452 


70.8823 


^ 


42.0189 


140.501 


Vs 


5-8905 


2.7612 


H 


8 . 0642 


25-9673 


5/8 


30.2379 


72-7599 


Az 


42.4116 


143.139 


2 


6.2832 


3.1416 


% 


[8.4569 


27.1086 


yi 


30.6306 


74.6621 


H 


42.8043 


145.802 


Ks 


6.6759 


3-5466 


6 


8.8496 


28.2744 


As 


31-0233 


76.5888 


Va 


43-197 


148.49 


H 


7.0686 


3-9761 


As 


9 2423 


29 . 4648 


10 


31.416 


78.54 


7/8 


43-5897 


151.202 


Vs 


7.4613 


4-4301 


A 


9-635 


30.6797 


J'8 


31.8087 


80.5158 


14 


43 9824 


153-938 


V2 


7-854 


4.9087 


H ■' 


20.0277 


31.9191 


Aa 


32.2014 


82.5161 


As 


44-3751 


156-7 


H 


8.2467 


5-4119 


Az • 


20 . 4204 


33-1831 


i^ 


32.5941 


84.5409 


Aa 


44-7678 


159-485 



32 



A MANUAL OF MECHANICAL DRAWING. 



Diam- 


Circum- 




Diam- 


Circum- 




Diam- 


Circum- 




Diam- 


Circum- 




eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


Vs 


45-1065 


162 . 296 


Vs 


58-5123 


272.448 


Vs 


71.8641 


410.973 


Vs 


85-21.59 


577-87 


V2 


45-5532 


165.13 


H 


58-905 


276.117 


23 


72.2568 


415-477 


Va 


85.6086 


583.209 


H 


45-9459 


167.99 


Vs 


59-2977 


279.811 


Vs 


72.6495 


420 . 004 


Vs 


86.0013 


588.571 


54 


46-3386 


170.874 


19 


59.6904 


283.529 


Va 


73.0422 


424.558 


V2 


86.394 


593-959 


Vs 


46.7313 . 


173.782 


Vs 


60.0831 


287.272 


Vs 


73.4349 


429.135 


Vs 


86.7867 


599-371 


15 


47-124 


176.715 


Va 


60.4758 


291.04 


V2 


73.8276 


AZZ-m 


Va 


87.1794 


604.807 


Vs 


47-5167 


179.673 


Vs 


60.8685 


294.832 


Vs 


74.2203 


438.364 


Vs 


87-5721 


610.268 


Va 


47-9094 


182.65s 


V2 


61.2612 


298.648 


Va 


74-613 


443-015 


28 


87.9648 


615-754 


Vs 


48.3021 


185.661 


Vs 


61.6539 


302.489 


Vs 


75-0057 


447-69 


Vs 


88.3575 


621.264 


V2 


48.6948 


188.692 


Va 


62 . 0466 


306.355 


24 


75.3984 


452.39 


Va 


88.7502 


626.798 


H 


49.0825 


191.748 


Vs 


62.4393 


310.245 


Vs 


75-7911 


457.115 


Vs 


89.1429 


632.357 


34 


49 . 4802 


194.828 


20 


62.832 


314.16 


Va 


76.1838 


461.864 


V2 


89-5356 


637-941 


Vs 


49.8729 


197.933 


Vs 


63.2247 


318.099 


Vs 


76.5765 


466.638 


Vs 


89.9283 


643-549 


16 


50.2656 


201.062 


Va 


63-6174 


322.063 


V2 


76 . 9692 


471.436 


Va 


90.321 


649.182 


H 


50.6583 


204.216 


Vs 


64.0101 


326.051 


Vs 


77.3619 


476.259 


Vs 


90.7137 


654.84 


Va 


51.051 


207.395 


V2 


64 . 4028 


330.064 


Va 


77.7546 


481 . 107 


29 


91 . 1064 


660.521 


H 


51.4437 


210.598 


Vs 


64-7955 


334.102 


Vs 


78.1473 


485-979 


Vs 


91.4991 


666.228 


V2 


51.8364 


213.825 


Va 


65.1882 


538.164 


25 


78.54 


490.875 


Va 


91.8918 


671.959 


H 


52.2291 


217.077 


Vs 


65.5809 


342.25 


Vs 


78.9327 


495.796 


Vs 


92.2845 


677.714 


V4 


52.6218 


220.354 


21 


65.9736 


346.361 


Va 


79.3254 


500.742 


V2 


92.6772 


683.494 


Vs 


53.014s 


223.655 


Vs 


66.3663 


350.497 


Vs 


79.7181 


505.712 


Vs 


93.0699 


689 . 299 


17 


53.4072 


226.981 


Va 


66.759 


354.657 


v. 


80.1108 


510.706 


Va 


03.4626 


695 . 128 


/8 


53-7999 


230.331 


Vs 


67.1517 


358.842 


Vs 


80.5035 


515.726 


Vs 


93.8553 


700.982 


% 


54.1926 


233.706 


V2 


67-5444 


363.051 


Va 


80.8962 


520.769 


30 


94-248 


706.86 


Vs 


54.5853 


237.105 


Vs 


67.9371 


367.285 


Vs 


81.2889 


525.838 


Vs 


94.6407 - 


712.763 


V2 


54-978 


240.529 


Va 


68.3298 


371.543 


26 


81.6816 


530.93 


Va 


95.0334 


718.69 


Vs 


55-3707 


243.977 


Vs 


68.7225 . 


3:5.826 


Vs 


82.0743 


536.048 


Vs 


95.4261 


724.642 


Va 


55.7634 


247.45 


22 


69.1152 


380.134 


Va 


82.467 


541.19 


V2 


95.8188 


730.618 


Vs 


56.1561 


250.948 


Vs 


69.5079 


384.466 


Vs 


82.8597 


546.356 


Vs 


96.2115 


736.619 


18 


56.5488 


254.47 


Va 


69.9006 


388.822 


V2 


83.2524 


551.547 


Va 


96 . 6042 


742.645 


Vs 


56.9415 


258.016 


Vs 


70.2933 


393.203 


Vs 


83-6451 


556.763 


Vs 


96.9969 


748.695 


Va 


57.3342 


261.587 


V2 


70.686 


397.609 


Va 


84.0378 


562.003 


31 


97.3896 


754.769 


Vs 


57.7269 


26s . 183 


Vs 


71.0787 


402 . 038 


Vs 


84-4305 


567.267 


v^ 


97.7823 


760.869 


V2 


58.1196 


268.803 


1 Va 


71.4714 


406.494 


27 


84-8232 


572.557 


Va 


98.175 


766.992 



A MANUAL OF MECHANICAL DRAWING. 



33 



Diam- 


Circum- 




eter. 


ference. 


Area. 


H 


98.5677 


773 U 


V2 


98.9604 


779-313 


H 


99-3531 


785-51 


Va 


99 7458 


791-732 


7/8 


00.1385 


797-979 


32 


too. 5312 


804.25 


'A 


00.9239 


810.545 


Ya 


01.3166 


816.865 


vi 


01.7093 


823.21 


'A 


02.102 


829.579 




02.4947 


835 -972 


Va 


02.8874 


842.391 


H 


03.2801 


848.833 


33 


03.673 


855-301 


-A 


04.065 


861.792 


Va 


04.458 


868.309 


H 1 


04.851 


874-85 


'A 


05.244 


881.415 


H 


05.636 


888.005 


Va 


06.029 


894-62 


H 


06.422 


901-259 


34 


06.814 


907 . 922 


H 


107.207 


914.611 


Vx 


IC7.6 


921.323 


Vs 


107.992 


928.061 


A 


[ 08. 385 


934.822 


V^ 


[08.778 


941.609 


Va 


[09. 171 


948.42 


% 


09.563 


955-255 


35 


[09.956 


962.115 


A 1 


10.349 


969. 


Va 


I 10. 741 


975-909 


Vs 


II. 134 


982.842 


A 


11.527 


989.8 



Diam- 
eter. 

H 
?4 

36 



A 

Va 
Vs 

37 



Va 

Vs 

38 

Vs 
Va 
Vs 
A 
A 
Va 
A 
39 



A 
A 
Va 



Circum- 




ference. 


.Area. 


III. 919 


996.783 


112. 312 


1003.79 


112.705 


1010.822 


113098 


1017-878 


113. 49 


1024.96 


113-883 


1032.065 


114.276 


1039-195 


114.668 


1046.349 


115. 061 


1053-528 


115-454 


1060.732 


115.846 


1067.96 


116.239 


1075-213 


116.632 


1082.49 


117.025 


1089.792 


117.417 


1097. 118 


117.81 


1104.469 


118.203 


nil. 844 


118.595 


III9.244 


[18.988 


1126.669 


119.381 


II34.II8 


"9-773 


II4I.59I 


120.166 


1149.089 


120.559 


II56.6I2 


120.952 


1 164. 159 


121.344 


II7I.73I 


121.737 


1179-327 


122.13 


1186.948 


122.522 


1194-593 


122.915 


1202 . 263 


123.308 


1209.958 


123.7 


1217.677 


24.093 


1225.42 


124.486 


1233.188 


124.879 


1240.981 



|! Diam- 
eter. 

A 

40 

As 
A 



Va 
A 

41 

As 
A 
Vs 

A 



42 
Vs 
Va 
Vs 
A 
H 
Va 
A 

43 

A 
A 



Va 
A 

44 



Circum- 




ference. 


Area. 


25.271 


1248.798 


25.664 


1256.64 


26.057 


1264.51 


26.449 


1272.4 


26.482 


1280.31 


27.235 


1288.25 


27.627 


1296.22 


28.02 


1304.21 


28.413 


1312.22 


28.806 


1320.26 


29.198 


1328.32 


29.591 


1336-41 


29.984 


1344-52 


30.376 


1352-66 


30.769 


1360.82 


31.162 


1369. 


31.554 


1377.21 


31-947 


1385.45 


32.34 


1393.7 


32.733 


1401.99 


33-125 


1410.3 


33.518 


1418.63 


33.911 


1426.99 


34 303 


1435.37 


34.696 


1443-77 


35-089 


1452.2 


35-481 


1460.66 


35-874 


1469.14 


36.267 


1477-64 


36.66 


1486.17 


37.052 


1494-73 


37-445 


1503-3 


37 -^3^ 


1511.91 


38.23 


1520.53 



Diam- 
eter. 

A 
Va 
H 
A 
A 
Vx 
A 
45 

A 
A 
A 
A 
A 
Va 
A 

46 

A 
A 
V& 
A 
H 
Va 
A 
47 

A 
A 
Vs 
A 
A 
Va 
A 

48 

A 
I Va 



Circum- 




fcrcnce. 


Area. 


138.623 


1529.19 


139.016 


1537.86 


[39.408 


1546-56 


139.801 


1555-29 


[40.194 


1564.04 


[40.587 


1572.81 


40.979 


1581.61 


41.372 


1590.43 


141-765 


159928 


142.157 


1608.16 


142.55 


1617.05 


142.943 


1625-97 


143.335 


1634.92 


143.728 


1643.89 


[44.121 


1652.89 


I4-I-514 


1661.91 


[44.906 


1670.95 


145-299 


1680.02 


145-692 


1689. II 


[46.084 


1698.23 


146-477 


1707.37 


[46.87 


1716.54 


47.262 


1725.73 


147.655 


1734-95 


148.048 


1744-19 


148.441 


1753-45 


148.833 


1762.74 


149.226 


1772.06 


149.619 


1781.4 


150.011 


1790.76 


150.404 


1800.15 


150.797 


1809.56 


151. 189 


1819. 


151.582 


1828.46 



34 



A MANUAL OF MECHANICAL DRAWING. 



Diam- 


Circum- 




Diam- 


Circum- 




Diam- 


Circum- 




Diam- 


Circum- 




eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


H 


51-975 


1837-95 


■^ 


165-327 


2175.08 


Vs 1 


78.678 


2540.58 


Vs 


192.03 


2934.46 


H ] 


52.368 


1847.46 


Ya 


165.719 


2185.42 


57 ] 


79.071 


2551-76 


V4 


192.423 


2946.48 


Vs ] 


52.76 


1856.99 


Vs 


166. 112 


2195-79 


Vs ] 


79.464 


2562.97 


Ys 


192.816 


2958.52 


M 


53153 


1866.55 


53 


166.505 


2206. I 9 


Va 


79-857 


2574-2 


V2 


193.208 


2970.58 


V» ] 


53-546 


1876.14 


Vs 


166.897 


2216.61 


Ys 


80 . 249 


2585-45 


Vs 


193.601 


2982.67 


49 


53-938 


1885-75 


Va 


167.29 


2227.05 


v. 


80 . 642 


2596-73 


Va 


193-994 


2994-78 


Vs 


54-331 


1895-38 


Y% 


167.683 


2237.52 


Ys ] 


81,035 


2608 . 03 


Vs 


194-386 


3006 . 92 


Va 1 


54-724 


1905.04 


V 


168.076 


2248.01 


■/ 


81.427 


2619.36 


62 


194.779 


3019.08 


Vs 3 


55-116 


1914-72 


Ys 


168.468 


2258.53 


Vs 


81.82 


2630.71 


Vs 


195-172 


3031-26 


% 1 


55-509 


1924-43 


Va 


168.861 


2269 . 07 


58 ] 


82.213 


2642 . 09 


Va 


195-565 


3043-47 


Ks 


55-902 


1934.16 


/s 


169.254 


2279 . 64 


Vs 


82.605 


2653.49 


Ys 


195-957 


3055-71 


34 


56.295 


1943-91 


54 


169.646 


2290 . 23 


Va 1 


82.998 


2664.91 


Vi 


196-35 


3067.97 


7/8 ] 


56.687 


1953-69 


Vs 


170.039 


2300.84 


Ys 


83-391 


2676.36 


Ys 


196-743 


3080.25 


50 ] 


57 -08 


1963-5 


V 


170.432 


2311.48 


V2 ] 


83-784 


2687.84 


Ya 


197-135 


3092.56 


Vs 


[57-473 


1973-33 


Vs 


170.824 


2322.16 


Ys 


84.176 


2699.33 


Vs 


197-528 


3104-89 


Va ] 


57-865 


1983-18 


V 


171. 217 


2332.83 


Ya 


84.569 


2710.86 


63 


197.921 


3117-25 


3/8 ] 


58.258 


1993 06 


Vs 


171. 61 


2343-55 


Vs ] 


84 . 962 


2722.41 


Vs 


198.313 


3129-64 


V2 


58-651 


2002 . 97 


Va 


172.003 


2354 -29 


59 


85-354 


2733-98 


Va 


198.706 


3142.04 


Ys 


59 -043 


2012.89 


Vs 


172.395 


2365-05 


Vs 


85-747 


2745-57 


Ys 


199.099 


315447 


Va 1 


.59-4.36 


2022.85 


55 


172.788 


2375-83 


Va 


86.14 


2752.2 


v 


199.492 


3166.93 


7/8 


59-829 


2032.82 


Vs 


173- 181 


2386.65 


Ys 


86.532 


2768.84 


Ys 


199.884 


3179-41 


51 


60.222 


2042,83 


Va 


173-573 


2397.48 


V 


86.925 


2780.51 


Ya 


200 . 277 


319I-91 


Vs 


[60.614 


2052.8s 


Y 


173-966 


2408.34 


Ys 


187-318 


2792 . 21 


Vs 


200 . 67 


3204.44 


Va 


61.007 


2062.9 


V 


174-359 


2419.23 


Ya 


187-711 


2803.93 


64 


201.062 


3217. 


Ys ] 


61.4 


2072 . 98 


Ys 


174-751 


2430.14 


Vs 


188.103 


2815.67 


Vs 


201.455 


3229.58 


V^ 


[61 . 792 


2083.08 


Ya 


175-144 


2441-07 


60 


188.496 


2827.44 


Va 


201.848 


3242.18 


Ys 


62.185 


2093.2 


7/8 


175-537 


2452.03 


Vs 


188.889 


2839-23 


Ys 


202 . 24 


3254-81 


Ya 


[62.578 


2103.35 


56 


175-93 


2463,01 


Va 


189-281 


2851-05 


V 


202.633 


3267-46 


Ys 


62.97 


2113.52 


Vs 


176.322 


2474,02 


Ys 


189.674 


2862.89 


Ys 


203 , 026 


3280.14 


52 


63-363 


2123.72 


Va 


176.715 


2485-05 


/2 


190.067 


2874 . id 


Ya 


203.419 


3292.84 


Vs 


63-7.56 


2133-94 


Ys 


177.108 


2496.11 


Ys 


190.459 


2886.65 


Ys 


203.811 


3305-56 


Va 


64 . 149 


2144.19 


v 


177-5 


2507.19 


Ya 


[90.852 


2898.57 


65 


204 . 204 


3318.31 


Ys 


64-54t 


2154.46 


Ys 


177-893 


2518-3 


Vs 


191 -245 


2910.51 


Vs 


204.597 


3331-09 


V2 


64-934 


2164.76 


Ya 


178.286 


2529-43 


61 


[91,638 


2922.47 


Va 


204 . 989 


3343-89 



A MANUAL OF MECHANICAL DRAWING. 



35 



Diam 


circum- 




Diam- 


Circum- 




Diam 


Circum- 




Diam 


Circum- 




eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


H 


205 • 382 


3356.71 


Vs 


218.734 


3807.34 


n 


232.086 


4286.33 


Vi 


245-437 


4793-7 


Vz 


205.775 


3369.56 


Va 


219.127 


3821.02 


74 


232.478 


4300.85 


)4 


245-83 


4809.05 


Vi 


206.167 


3382.44 


'A 


219.519 


3834.73 


% 


232.871 


4315-39 


Vi 


246.223 


4824.43 


H 


206.56 


3395-33 


70 


219.912 


3848-46 


Va 


233 264 


4329-96 


V2 


246.616 


483983 


% 


206.953 


3308.26 


A 


220.305 


3862.22 


V» 


2.33.656 


4344-55 


v% 


247.008 


4855 26 


66 


207.346 


3421-2 


Va 


220 . 697 


3876. 


V2 


234.049 


4359-17 


Va 


247-401 


4870.71 


/s 


207.738 


3434.17 


Vs 


221.09 


3889-8 


H 


234.442 


4373-81 


n 


247-794 


4886.18 


% 


208.131 


3447.17 


H 


221.483 


3903-63 


¥a 


234.835 


4388.47 


79 


248.186 


4901.68 


H 


208.524 


3460.19 


5/8 


221.875 


3917-49 


/8 


235.227 


4403.16 


Vs 


248.579 


4917.21 


'A 


208.916 


3473-24 


Va 


222 . 268 


3931-37 


75 


235.62 


4417-87 


Va 


248.972 


4932.7s 


H 


209.309 


3486.3 


Vs. 


222.661 


3945-27 


% 


236.013 


4432.61 


Vs 


249.364 


4948.33 


V4 


209 . 702 


3499-4 


71 


223.054 


3959-2 


Va 


236.405 


4447-38 


V2 


249 -757 


4963.92 


n 


210.094 


3512.52 


A 


223.046 


3973-15 


V% 


236.798 


4462.16 


54 


250.1s 


4979. 55 


67 


210.487 


3525.66 


Va 


223.839 


3987-13 


V2 


2.37. 191 


4476.98 


Va 


250.543 


4995.19 


H 


210.88 


3538.83 


H 


224.8.32 


4001 . 13 


?/s 


237.583 


4491.81 


Vs 


250.935 


5010.86 


Va 


211.273 


3552.02 


V2 


224.624 


4015-16 


Va 


237-976 


4506.67 


80 


251-328 


5026.56 


H 


211.665 


3565.24 


5-^ 


225.017 


4029.21 


Vz 


238.369 


4521.56 


Vs 


251.721 


5042.28 


V2 


212.058 


3578.48 


Va 


225.41 


4043-29 


76 


238.762 


4536.47 


Va 


252.113 


5058.03 


H 


212.451 


3591.74 


n 


225.802 


4057-39 


Vz 


239-154 


4551.41 


Vs 


252.506 


5073.79 


Va 


212.843 


3605.04 


72 


226.195 


4071 -SI 


Va 


239.547 


4566.36 


V2 


252.899 


5089.59 


% 


213.236 


3618.35 


Ks 


226.588 


4085-66 


H 


239-94 


4581.35 


Vs 


253.291 


5105.41 


68 


213.629 


3631.69 


Va 


226.981 


4099.84 


]/-, 


240.332 


4596.36 


Va 


253.684 


5121.25 


Vi 


214.021 


3645.05 


H 


227.373 


41 14 04 


Vs 


240.725 


4611.39 


% 


254.077 


5137.12 


Va 


214.414 


3658.44 


V2 


227 . 766 


4128.26 


Va 


241.118 


4626.45 


81 


254.47 


5153.01 


H 


214.807 


3671.86 


5/8 


228 . 1 59 


4142.51 


% 


241.151 


4641.53 


K 


254.862 


5168.93 


H 


215.2 


3685.29 


Va 


228.551 


4156-78 


77 


241-903 


4656.64 


Va 


255.255 


5184.87 


H 


215.592 


3698.76 


% 


228.944 


4171.08 


/8 


242 . 296 


4671.77 


Vs 


255.648 


5200.83 


Va 


215.985 


3712.24 


73 


229-337 


4185-4 


Va 


242 . 689 


4686 . 92 


V2 


250.04 


5216.82 


% 


216.378 


3725-75 


Vk 


229.729 


4199.74 


H 


243.081 


4702.1 


Vs 


256.433 


5232-84 


69 


216.77 


3739-29 


Va 


230.122 


4214. II 


V2 


243 -474 


4717.31 


Va 


256.826 


5248.88 


Vi 


217.163 


3752-85 


Vi 


230.515 


4228.51 


% 


243-867 


4732.54 


Vs 


257.218 


5264.94 


Va 


217.556 


3766.43 


/2 


230.908 


4242-93 


Va 


244 259 


4747-79 


82 


2£7. 611 


5281.03 


^ 


217.948 


3780.04 


V% 


231.3 


4257-37 


Vs 


244.652 


4763-07 


Vs 


258.004 


5297.14 


V2 


218.341 


3793-68 


Va 


231.693 


4271.84 


78 


245-045 


4778-37 


Va 


258.397 


5313.28 



36 



A MANUAL OF MECHANICAL DRAWING. 



Diam 


■ Circum- 






Diam 


Circum- 




Diam 


Circum- 




Diam 


Circum- 






eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


eter. 


ference. 


Area. 


Vs 


258.789 


5329-44 


Vs 


272.141 


5893-55 


H 


285.493 


6486.04 


% 


298.845 


7106.9 


'A 


259.182 


5345 


63 


Va 


272.534 


5910.58 


91 


285.886 


6503-9 


V 


299.237 


7125 


59 


H 


259-575 


5361 


84 


Vs 


272 . 926 


5927.62 


Vs 


286.278 


6521.78 


Vs 


299.63 


7144 


31 


V4 


259.967 


5378 


08 


87 


273-319 


5944-69 


Va 


286.671 


6539-68 


V2 


300.023 


7163 


04 


Vs 


260.36 


5394 


34 


Vs 


273-712 


5961.70 


Vs 


287 . 064 


6557-61 


Vs 


300.415 


7181 


81 


83 


260.753 


5410 


62 


Va 


274-105 


5978.91 


V2 


287.456 


6575-56 


Va 


300.808 


7200 


6 


Vs 


261 . 145 


5426 


93 


Vs 


274.497 


5996.05 


Vs 


287.849 


6593 - 54 


Vs 


301. 20T 


7219 


41 


54 


261.538 


5443 


26 


V2 


274-89 


6013.22 


Va 


288.242 


6611.55 


96 


501 . 594 


7238 


35 


Vs 


261.931 


5459 


62 


Vs 


275-283 


6030.41 


Vs 


288.634 


6629.57 


Vs 


301.986 


7257 


II 


V2 


262 . 324 


5476 


01 


Va 


275-675 


6047-63 


92 


289 . 027 


6647.63 


Va 
Vs 
Vi 


302.379 


7275 


99 


Vs 


262.716 


5492 


41 


H 


276.068 


6064 . 87 


Vs 


289 . 42 


6665.7 


302.772 
303-164 
303-557 


7294 
7313 
7332 


91 
84 
8 


34 


263.109 


5508 


84 


88 


276.461 


6082.14 


Va 


289.813 


6683.8 


/ ^ 

Vs 


Vs 


263.502 


5525 


3 


Vs 


276.853 


6099.43 


Vs 


290.205 


6701.93 


Va 


303-95 


7351 


79 


84 


263.894 


5541 


78 


Va 


277-246 


6116.74 


V2 


290.598 


6720 . 08 


Vs 
97 

Vs 
% 


304-342 


7370 


79 


Vs 

V4 


264.287 
264.68 


5558 
5574 


29 
82 


Vs 
V2 


277.629 
278.032 


6134.08 
6151-45 


Vs 
Va 


290.991 
291.383 


6738.2s 
6756-45 


304 -735 
305 - 128 
305-521 


7389 
7408 
7427 


83 
89 
97 


Vs 


265.072 


5591 


37 


Vs 


278.424 


6168.84 


Vs 


291 . 776 


6774.68 


Vs 


305-913 


7447 


08 


V2 


265.465 


5607 


95 


Va 


278.817 


6186.25 


93 


292.169 


6792.92 


V2 
Vs 
Va 
Vs 


306.306 
306.699 
307-091 
307.484 


7466 


21 


Vs 


265.858 


5624 


56 


rs 


279.21 


6203 . 69 


Vs 


292.562 


6811.2 


7485 
7504 
7523 


55 
75 


H 


266.251 


5641 


18 


89 


279 . 602 


6221.15 


Va 


292.954 


6829.49 


Vs 


266.643 


5657 


84 


Vs 


279-995 


6238 . 64 


Vs 


293-347 


6847-82 


98 


.307-877 


7542 


98 


85 


267.036 


5674 


51 


Va 


280.388 


6256.15 


V2 


203-74 


6866.16 


Vs 


308.27 


7562 


24 


Vs 
Va 


267.429 
267.821 


5691 
5707 


22 
94 


Vs 
V2 


280.78 
281.173 


6273.69 
6291 . 25 


Vs 
Va 


294-132 
294-525 


6884.53 
6902.93 


Va 
Vs 
V- 


308 . 662 
309-055 
309.448 


7581 
7600 
7620 


52 
82 
15 


Vs 


268.214 


5724 


69 


Vs 


281 . 566 


6308.84 


Vs 


294.918 


6921.35 


Vs 


309-84 


7639 


5 


Vz 


268.607 


5741 


47 


Va 


281.959 


6326.45 


94 


295-31 


6939-79 


Vx 


310.233 


7658 


88 


Vs 

Va 


268 . 999 
269.392 


5758 
5775 


27 
I 


Vs 

90 


282.351 
282.744 


6344.08 
6361.74 


Vs 
Va 


295-703 
296 . 096 


6958.26 
6976.76 


Vs 
99 

Vs 


3 TO. 626 
311.018 
311. 411 


7678 
7697 
7717 


28 
71 
16 


Vs 


269.785 


5791 


94 


Vs 


283.137 


6379-42 


H 


296.488 


6995.28 


V. 


3II.R04 


nz^ 


63 


86 


270.178 


5808 


82 


V4 


283.529 


6397-13 


V2 


296.881 


7013-82 


Vs 


312.196 


7756 


1^ 


Vs 


270.57 


5825 


72 


Vs 


283.922 


6414.86 


Vs 


297.274 


7032-39 




312.589 
312.982 
313-375 


7775 
7795 
7814 


66 

21 


Va 


270.963 


5842 


64 


V2 


284.315 


6432 . 62 


Va 


297 . 667 


7050.98 


/s 
Va 


78 


Vs 


271.356 


5859 


59 


H 


284.707 


6450.4 


Vs 


298.059 


7069.59 


Vs 


313-767 


7834 


38 


V2 


271.748 


5876 


56 


Va 


.'J85.I 


6468.21 


95 


298 . 452 


7088.23 


100 


314.16 


7854 





A MANUAL OF MECHANICAL DRAWING. 



37 



To ascertain circumference of other circles than those in 
table multiply the diameter in inches by 3.1416. 

To ascertain the area of other circles than those in table, 
multiply the square of the diameter in inches by .7854. 

To ascertain the area of a circular ring, subtract area of 
inner diameter from the area of outside diameter. 

To ascertaii solidity in cubic inches of a cylinder, multiply 
area of one end in square inches by the length of the cylinder 
in inches. 

To ascertain solidity in cubic inches of a hollow cylinder, 
subtract the area of the inside diameter in square inches from 
the area of the outside diameter in inches, and multiply the 
remainder by the length of cylinder in inches. 

To find the weight in pounds of a hollow cylinder of cast 
iron, multiply the solidity in cubic inches by .26. 

Example. — Find the weight of a cylinder of cast iron whose 
dimensions are : 

Outside diameter, 34" ; inside diameter, 24" ; length, 36". 



By table, area 34 inches 907.922 square inches. 
" 24 " 452.39 



Multiply by length 



455-532 

36 inches. 



solidity in cubic inches. 



2733192 
1366596 

16399.152 =- 
.26 

98394912 
32798304 



4263.77952 = weight in pounds. 
If the cylinder were made of brass the multiplier would be 
.291, instead of .2(>, as above. 



38 



A MANUAL OF MECHANICAL DRAWING. 



TABLE IV. 
Ultimate Resistance to Tension (Tensile Strength) in Pounds per Square Inch. 



Aluminum bronze, io% al. and 90% 
copper 

Aluminum bronze, i/4% al. and 9SH% 
copper 

Brass, cast . . . . , 

Brass wire 

Bronze or gun metal 

Copper, cast 

Copper, sheet 

Copper bolts 

Copper wire (unannealed) 

Iron, cast, 13,400 to 29,000 

Iron, wrought, round or square bars, 
I to 2 inch diameter, double refined. . . 50, 

Iron wire 7°: 

Iron wire ropes 

Lead, sheet 

Steel 65: 

Tin, cast 

Zinc 7 

Weights per Cubic Foot of Various 

Aluminum 

Anthracite, solid 

Anthracite, broken, loose 

Anthracite, broken, shaken 

Anthracite, heaped, bushel 

Brass, cast 

Brass, rolled 

Brick, pressed 

Brick, common, hard 



Average. 

85,000 lbs. 

28,000 lbs. 
18,000 lbs. 
49,000 lbs. 
36,000 lbs. 
19,000 lbs. 
30,000 lbs. 
36,000 lbs. 
60,000 lbs. 
16,500 lbs. 

000 to 54,000 lbs. 

,000 to 100,000 lbs. 

90,000 lbs. 

3,300 lbs. 
,000 to 120,000 lbs. 

4,600 lbs. 

,000 to 8,000 lbs. 

Substances. Lbs. 

162 

93 

54 

58 

80 

504 

524 

150 

-". 125 



Lbs. 

Brick, soft, inferior 100 

Brick, laid in wall, pressed 140 

Brick, laid in wall, common 112 

Coal, bituminous, solid 84 

Coal, bituminous, broken, loose 49 

Coal, bituminous, heaped bushel 74 

Copper, cast 542 

Copper, rolled. 548 

Gold, cast, pure, or 24 carat 1,204 

Gold, pure, hammered 1,217 

Iron, cast 450 

Iron, wrought 480 

Lead .... 711 

Granite 170 

Limestone and marble 168 

Mercury, at 32° Fahr 849 

Platinum i,342 

Silver 655 

Steel 490 

Tin, cast 459 

Water, pure rain, at 60° Fahr 62H 

Water, sea 64 

Zinc or spelter 43.7 

Weights per Cubic Inch. l^- 

Aluminum 0937 

Brass, cast 291 

Brass, rolled 303 

Bronze, cast 315 

Copper, cast , 313 



A MANUAL OF MECHANICAL DRAWING. 



39 



Lb. 

Copper, rolled 317 

Tin 265 

Zinc 260 

Lead 411 

Platinum 776 

Silver 379 

Gold 696 

Iron, cast 261 

Iron, wrought 281 



Lb. 

Steel 283 

Rubber 0338 

To obtain weight per cubic inch of other substances, divide 
weight given in table for one cubic foot by 1,728. 

Note. — In figuring the weight of castings of iron it is usual 
to add to the weight calculated from the drawing from 5% 
to 10%, to make up for "straining" of the casting in the sand 
or mould, the allowance depending upon the nature of the 
casting. 



TABLE V. 
Stand.\rd Key Seats. 




Diameter of Shaft. 
" to \\" inclusive. 



1//' ' 


ir 


Mr ' 


2 J// 


vr ' 


2a// 


m" • 


3 J// 


8^-' • 


sr 


afr • 


4 J" 


H^" ' 


4|// 



1 



c 


Diameter of Shaft. 


^ 


4}r 


' oj" inclusive 


8 


SfV 


' 5r 


* 


5|r 


' 6i" 




e/r 


. 7 J// 


1 


7A'' 


< 8i'/ 


1 


8fr 


. 9 J// 


1 


9^'^ 


. loj'/ 


14 1 


lOxV 


' Hi" " 



A 


B 


c 


li 


'y. 






i 


1] 


u 


, 


1 


1} 


i 


1 i 


2 


■ 


1 : 


2i 


i 


1 r 


2| 


i 


1 ; 


i 


U 



40 



A MANUAL OF MECHANICAL DRAWING. 



CHAPTER V. 



Plate i. The Planes of Projection and Projections. 



A solid of any desired form can be shown in many- 
different views, which, summed up, are the plan — 
upper and under — and the elevation, end and side or 
longitudinal. 

The names given to the views are according to the 
positions from which the object is seen. These are 
clearly shown in the several views of a cube ( Plate i ) . 
In the upper left hand corner is shown a perspective 
(isometrical) of the cube, with its several faces num- 
bered ; the sides imm.ediately in front or full view are 
represented by full lines and figures, while the sides or 
faces at the back are shown by dotted lines and figures. 
This figure is given for the purpose of showing the re- 
lation the several sides bear to each other, and by com- 
paring with the figures in projection it will be seen 
clearly the positions taken by the object in bringing its 
different sides into view. 

Front Elevation. — The central figure shows a cube 
resting on one of its edges, the sides taking the direc- 
tion of 45° to the horizontal. Being a cube, all the faces 
are squares, and all its edges of equal length ; therefore 
the dimensions being known the figure would be drawn 
as follows : First draw a circle whose diameter is equal 
to the length of a side, next with T square and 45° 



triangle draw the sides 2-3-4-5 tangent to the circle and 
intersecting at the corners. This completes the front 
elevation. 

Left Side Elevation. — With T square project the 
corners a-b-c to the left and measure oif the length 
of a side and draw lines i and 6 completing the figure, 
showing the sides 4 and 2. 

Right Side Elevation. — Project corners a-d-c and 
complete figure as for left side elevation, thus showing 
sides 3 and 5. 

Plan' or Top View. — Project corners b-a-d upward, 
using the 90° angle, and complete figure as in eleva- 
tions, giving sides 4 — 5. 

Inverted Plan. — Project corners b-c-d downward 
and complete figure by measuring oif the length of a 
side on the projected lines, and draw lines 6 and i, 
thus giving view of sides 2 and 3. 

In the foregoing figures or views of the cube all the 
sides are brought into view except side 6. The figure 
being a cube, this side would be exactly the same as 
side I, but should there be some peculiarity in this side, 
such as a depression, it could be shown by making a 
rear elevation, which would be a continuation of the 
projection of either side elevation, which would bring 



PLATE I 






6 




1 








5 


^ 


i K 




' / \ ' 


i ^/^'V X 1 


l/f '-'' '^^ \l 




1 *3\ ^/ X ' 
1 \ ~" X ' 


i ___ \sZ_ _1 


1 


'i^\ ■> 




\ 


2 


3 


1 

1 


1 

1 




41 



42 



A MANUAL OF MECHANICAL DRAWING. 



into view another square on which would be marked 
the Hues defining the depression, while its depth would 
be laid off on the elevations and plans, as shown by 
dotted lines. The depression could also be shown by 
dotted lines on front elevation, the fact of the lines 
being dotted indicating that the form shown is behind 
the face or front of the figure. In making a drawing, 
the principal face or view of the object to be repre- 
sented is first drawn, and the other views necessary to 
show the form fully are derived from it and placed in 
the positions that will most clearly show the form re- 
quired. Thus, should it be desired for some reason to 
show a full view of side 3, the lines a-d and b-c would 
be prolonged or projected, as indicated, and a square 
completed upon these projected lines would be a full 
view of the side. These same methods are followed in 
all the succeeding lessons. For convenience the plan is 
sometimes placed above and sometimes below the ele- 
vation, depending upon what is to be shown, and in all 
cases the most direct method is employed. This should 
be the aim of the draughtsman — to follow the shortest 
method that will fully explain his object. 

Plate 2. Projections of a Rectangular Prism 
AND Cube. 

Fig. I. — ^A rectangular prism, whose sides or faces are 
each I inch (i") wide and 2 inches (2") long is first 
drawn in end elevation, as shown at a-h-c-d. In this 



case the prism is resting upon one of its faces, and is 
drawn as follows : Draw a circle i" diam., and with T 
square and 90° angle draw the four sides tangent to 
the circle to complete the elevation. 

To draw the plan, project sides a c and h d, in- 
definitely, as indicated by the arrow heads, using 90° 
angle ; with T square draw side e f, in required position, 
from e or f lay off the length 2" as at h, and with T 
square draw g h, completing the plan. To complete an 
elevation showing the other end of the prism, continue 
the projection indefinitely, as indicated, and draw i k 
in desired position ; with i k for radius and i and k as 
centres, draw the arcs at / and m, connect / and m, or 
measure i I equal to i k, and with T square draw / m. 

Fig. 2. — The same prism is shown in end elevation, 
but in this case it is resting upon one edge, with its 
sides placed at the angles of 30° and 60° to the hori- 
zontal. As for Fig. I, first draw a circle of i" diame- 
ter and tangent to this circle draw the four sides of the 
square, using the 30° and 60° angles as indicated. The 
plan is drawn as in Fig. i, except that two sides of the 
prism will show ; therefore the three corners or angles 
will need to be projected as at e, f and g. The elevation 
of the opposite end is drawn exactly as for Fig. i, only 
the 30° and 60° angles are to be used instead of the 90° 
angle. The pupil must clearly fix in his mind the rela- 
tion that each of these views bears to the other, and for 
this purpose should use Plate i to aid him to establish 
this relation. 





-••' :. >-l 






y 




^t! 


• 


1 




1 

V 



1 


1 

1 






1 
wi 

1 


i 


1 
1 

i 
1 





44 



A MANUAL OF MECHANICAL DRAWING. 



Fig. 3. — A cube resting upon one of its edges with 
sides at angles of 45° to horizontal. In one face of the 
cube is a depression i" square, ^" deep, while in the 
centre of this depression is a further depression, round 
•J" diameter, -J" deep, the cube being i^" square on 
each face. 

First draw a circle ij" diameter and two others i" 
and ^" diameter, respectively, using the same centre for 
all, or in other words make the circles concentric. 

With 45° angle draw the sides of the cube, also of 
the square depression, making their sides tangent to 
the circles ; this completes the elevation. To draw the 
plan, project the corners or angles, as indicated, and 
mxcasure the length of a side, as shown, and with 
T square draw lines representing the faces. Project 
the angles of the depression and measure its depth from 
the face J", and draw line defining this depth. Project 
lines tangent to the inner circle, which represents the 
round depression, measuring its depth i" from face of 
cube, and draw with T square the line representing the 
bottom of this depression. As both of these depressions 
are within the cube, the lines indicating them would be 
dotted to show that they define something behind the 
surface. 

Plate 3. Projections of the Triangular Prism. 

Fig. I. — A triangular prism, whose sides are all equal, 
and consequently the ends of which are equilateral tri- 



angles, is to be shown in end and side elevations and in 
plan. 

With T square draw the side b-c of the required 
length, and with b-c as radius and b and c for centres 
sweep arcs intersecting at a, draw a-b and a-c, complet- 
ing the end elevation. Project a and c to the right in- 
definitely, measure a'-j equal to length of prism and 
draw a'-c' and j-k to complete the side elevation. 

With c for centre draw arcs c'-c" and k-h and tan- 
gent to these arcs, using T square, draw c" &" and h-g, 
with 90° angle draw or project b-a and c downward, 
connecting b" g, a" I and c" h, completing the plan. 
This method places the side elevation and plan at equal 
distances from the end elevation. If this is not re- 
quired, draw b" c" , as may be necessary; using T 
square, as before, project b-a and c and measure off 
b" g equal to c' k, and with T square draw g-h. 

In the elevation dimension a'-c' does not show the 
true width of the side a-c. With c for centre and c'-a' 
for radius, draw arc cutting a-c at /. The difference 
a-f between a-c and f-c will be amount of the fore- 
shortening, and this will vary, according to the angle 
at which the side a-c may be placed. From this it is 
seen that objects to be represented true to size by pro- 
jection must be represented by views so placed that 
when possible surfaces will be perpendicular to each 
other. This is shown in Fig. 2, which represents a 
triangular prism in end elevation. In one side or face 
of this prism is a depression ■^" deep, round bot- 



PLATE 3 




45 



46 



A MANUAL OF MECHANICAL DRAWING. 



tomed f " wide, round at one end and square at the 
other end ; a line passing through the centre of this 
depression is ■^" off the centre of the prism. The 
round end of the depression is ^" from the end of the 
prism, while the opposite ends are ■^" apart. The 
depression is i^" long, the prism i^" long, and the 
centre from which the round end of depression is drawn 
is 3^" from the end of the prism. 

If this were shown on the side elevation of Fig. i, 
all the dimensions of width would be foreshortened, 
and therefore not in true proportion to the length. 

In Fig. 2 the side a-c is projected perpendicularl.y, 
therefore all the dimensions of zvidth, as well as length, 
can be correctly measured and laid out, while the dotted 
semi-circle in the end elevation defines the form and 
depth of the depression. The end elevation of the 
prism being an equilateral triangle, the side a-c would 
be drawn with the 6o° angle ; consequently all lines 
projected with the 30° angle from a-c would be perpen- 
dicular to a-c. With this explanation the pupil should 
be able to work out this lesson. It must not be under- 
stood that all the information given in Fig. 2 cannot 
as well be conveyed by Fig. i. It can, and in the ma- 
jority of cases would be, but in that event all the dimen- 
sions of width would be taken from the end elevation, 
and would not be so clear. There are many cases where 
the method shown in Fig. 2 would be necessary, because 
the forms to be shown would be too intricate to be 
safely shown otherwise. 



In Fig. 3 is given another illustration of the effect of 
foreshortening. In this case all dimensions would be 
taken from the end elevation and plan, as no measure- 
ments could be taken from the side elevation. To draw 
this exercise, first lay out the plan to any required di- 
mensions, and by projecting a-b and c, as indicated by 
the arrow heads, and complete as in Fig. i.- Project 
a-h-c-f-j-h and g, using 90° angle, draw a' g\ using T 
square. Make /' / and /' in each equal to half a-c, with 
radius l-in and / and m for centres, sweep arcs cutting 
at e', through e' and parallel with a' g' draw b' W , 
draw b' a', b' c' , e' f and h' g'. 



Plate 4. Projections of a Cube Standing Upon 
One of Its Corners. 

First draw the centre lines of the plan, and on them 
a circle whose diameter is equal to the side of a face, and 
complete the plan by drawing with 45° triangle sides, 
5" — 6", 6" — 5'", 5'" — 4" and 4" — 5". Project corners 
6" — 5" — 4" upwards (using 90° angle), then with 30° 
angle draw 5 — 4 and 5 — 6. Make 5 — 7 equal to 5 — 4, 
with 7 as centre and rad. 5 — 7 draw circle which will 
circumscribe the hexagon representing the cube. With 
30° angle draw i — 2, 2—t„ 3 — 7, 7—1, and with 90° 
angle draw i — 6 and 3 — 4. With T square project 
points 2 — 3 — 4 — 5 and 7 to the right. Take point 5' 
on line with 5 — 5' as centre and radius equal to diagonal 



PLATE 4 




Pla//. 



€VAT/0A/, 



47 



A MANUAL OF MECHANICAL DRAWING. 



6" — 4" in plan, mark off point 7' on line 7 — 7', 
draw 5' — 4' — 7'. Projection of point 4 will cut 
line 5' — 7' at its middle 4', draw 4' — 3' per- 
pendicular to 5' — 7' and 2! — 7' and 5' — 7" paral- 
lel to 4' — 3', draw 2' — 7" through 3', thtis completing 
the front and side elevations. To draw the fourth 
figure or elevation, project the points 5" — 4" and 5'" to 
the right, using the T square, then with 90° angle pro- 
ject point 7" to c, 3' to a and produce to /, 2' to h and 
produce to d and g, and 7' to e. Connect c-a, c-f, a-d, 
d-f, a-b, d-e, f-g, b-e and e-g. 

Note. — In all of these lessons the student should use 
the T square for all horizontal lines, and the 90" angles 
for perpendicular or vertical lines; 30°-6o° and 45° 
angles are to be drawn with the 30°-6o° and 45° sides 
of the triangle, using the T square as the base upon 
which to guide the triangles. 



Plate 5. Projections of an Hexagonal Prism. 

Draw centre lines A B and c-f. With their inter- 
section g as centre, draw circumscribing circle of re- 
quired diam., then with 60° angle draw c-b, c-d, a-f and 
f-e, and with T square draw b-a and d-e, completing 
the plan. 

With 90° angle project corners c-d-e-f to m-n-o-p, 
and draw base line m-p, lay off from scale the re- 



quired height of prism m-h, and draw h-l, thus com- 
pleting the front elevation. 

Draw side i — 2 of side elevation and produce to in- 
tersect with d-e of plan produced; through this inter- 
section with 45° angle draw line 7 — 8 — 9, produce b-a 
and c-/ until they intersect line 7 — 8 at 9 and 8. With 
90° angle project points of intersection 8 and 9 to 3 — 4 
and 5 — 6, and with T square draw i — 5 and 2 — 6 con- 
tinuations of h-l and ni-r, completing side elevation. 

Now suppose it necessary to draw a side elevation 
inclined toward observer and at an angle of 60° to the 
horizontal. With the 30° angle project the angles or 
corners of the upper and lower faces of the front ele- 
vation until they intersect a line C d drawn at the angle 
of 60° to the horizontal. Through C draw C E perp. 
and F T horizontal. With C as centre sweep arcs H I, 
J K, L M, N O, P O, R S and D E, thus transferring 
the points from C D to C E. Lay off C G, G T equal 
to 2 — 4, 4 — 6, and through C, G and T draw indefinite 
perpendiculars. With T square project C, M, O and 
E to G, M', O' and E', and I, K, O and S to I', K', 
Q' and S'. Connect these points, as shown in plate, 
completing the inclined front elevation. To transfer 
the dimensions of width in the plan to the side eleva- 
tion, a second method is shown in which the compass is 
used as indicated by the dotted arcs. Any convenient 
point can be used for the centre from which to sweep 
these arcs, as at 7 ; the arcs must be drawn tangent to 
the lines projected from a, f and e of the plan. 



PLATE 5 




Front ^LOVATior/. 



p: _ _ 



C 1 fl T 

5lDE f-l^aVATlOt/ 

/fVCLINED. 



5/OC ELCVAT/Ot^ 



49 



50 



A MANUAL OF MECHANICAL DRAWING. 



Plate 6. Projections of an Hexagonal Pyramid, 

WHICH IS Standing Upon One Corner, 

AND Whose Centre Line is Inclined 

30° FROM the Vertical. 

Draw centre line A B, at angle of 60° to the hori- 
zontal or 30° from the vertical, using 60° side of tri- 
angle, and upon it draw a circle of a size to circum- 
scribe the hexagonal base of the pyramid. With 30° 
and 90° angles draw diameters D G, E H and C F ; also 
with the same angles draw sides C D, D E, E F, F G, 
G H and H C. This completes the plan. 

With 60° angle project the angles or corners E, F, 
G and H of the plan downward and parallel with 
centre line A B to I, J, K and L, and with 30° angle 



draw base line I L perpendicular to A B. Measure 
off the height of the pyramid along the centre line from 
B to M, and draw M I, M J, M K, M L, completing 
the side elevation. With 30° angle project angles D, 
E and F indefinitely to the left, and with U as centre 
draw indefinite arcs and with 90° angle draw tangent 
to these arcs indefinite lines to P, O and O. With T 
square project points I, J, K and L horizontally inter- 
secting the vertical lines at T, R, S, P, O and O. 
Draw T R, R P, P O, O Q, Q S and S T. "with 90° 
angle draw indefinitely O N. With T square project 
the vertex of the pyramid to the left, intersecting O N 
at N. Draw N R^ N P, N O, N S. The sides R T 
and T S of the base being behind or on the side oppo- 
site the observer, would be dotted as shown. 



PLATE 6 



r: 






\^''^ 


y' 


>^ 





^ 


\ 








1 


\ 


^ 


\ 

\ 


^ 


^ 


^ \s\ 






^^^ 


\ " 


^^\^ 


- - 


— A 


- " - >-s 




51 



52 



A MANUAL OF MECHANICAL DRAWING. 



Plate 7. Projection of a Cylinder Whose Axis is 
Inclined at an Angle of 30" to the Vertical. 

With 60° angle draw centre line A B, and at right 
angles to A B, using 30° angle, draw centre line C D. 
With O as centre and radius equal to half diam. of 
cylinder draw circle A C W D. This will be the plan of 
the cylinder. 

With 30°-6o° and 90° angles divide the semi-circum- 
ference into six equal parts, C E, E F, F W, W G, G H, 
H D, and with 60° angle project points C, E, F, G, H 
and D downward indefinitely, and with 30° angle draw 
base line J P. Measure off centre line B S equal to 
height of cylinder and draw P S V, completing side 
elevation. 

At suitable distance to the right of side elevation 
draw centre line A' B', and on it draw a semi-circle 
with radius equal to O C, and with 30°-6o° angles and 



T square divide into six equal parts as indicated in 
dotted lines on front elevation at i, 2, 3, 4, 5, 6, 7, and 
through these points draw with 90" angle indefinite 
lines parallel with A' B'. Now with T square project 
points P, O, R, S, T, U, V and J, L, M, B, N, O, P 
to the right, intersecting the lines drawn through i, 2, 
3, etc. These intersections are points in a curved line 
forming an ellipse, which should be lightly and 
smoothly drawn in by hand and afterwards drawn 
firmly by means of irregular curves. This completes 
the front elevation. This and the following lessons 
show curves developed by intersecting lines, and all 
make the use of the irregular (sometimes called French 
curves) necessary, and the student should endeavor to 
acquire skill in using them. As an aid to the fitting of 
the curves to the points the lines should be sketched in 
freehand, but lightly. 



PLATE 7 




63 



54 



A MANUAL OF MECHANICAL DRAWING, 



CHAPTER VI. 



Plate 8. Conic Sections — The Parabola. 



The parabola is a curve which is formed by a 
plane which cuts a cone in a line parallel with one of 
its sides, and is a curve of which any point is equally 
distant from a fixed point, called its focus, and from a 
given straight line called the directrix. (See Fig. 14, 
Plate II.) 

To develop the parabola from a cone: 

Draw the centre lines A B and C D. With their 
point of intersection O for centre and radius equal to 
radius of the base of the cone draw the circle, A C J D, 
which will be the plane of the cone. 

With 30°-6o° and 90° angles divide the base into 
six equal parts, as i, 2, 3, etc. 

Lay off distance J B equal to height of cone, and 
through B draw E F, making B E equal to O C and 
B F equal to O D, and draw J E and J F to complete 
side elevation of cone. 

Project points i, 2, 3 upon the base E F as i', 2', 3', 
and draw lines Ji', J2', J3'. Draw G H parallel with 



J F. G H represents the cutting plane. Perdendicu- 
lar to G H and from the points of intersection of G H 
with the lines drawn from the vertex J of the cone to 
its base E F, draw the indefinite lines, a, b, c, d, e, f, 
and at L draw L K parallel with G H. 

Returning to the plan : through the centre O draw 
the diameters from points i, 2, 3, etc., and onto these 
diameters project the points of intersection of G H 
with Ji', J2', J3', as shown at gg', hh', JJ', etc. These 
points are points through which the plan of the para- 
bola is to be drawn, and all are determined lay the in- 
tersections of the lines, except O J and O J'. Where 
the plane G H intersects the centre line J B of the cone 
draw M N parallel with the base, JJ' is equal to M N. 

To complete the elevation of the parabola, with the 
compasses transfer the distances gg', hh', etc., to 44', 
55', etc., laying out equally each side of K L on the 
lines a, b, c, etc. Through the points thus found draw 
the curve. 



PLATE 8 




56 



56 



A MANUAL OF MECHANICAL DRAWING. 



Plates 9 and 10. The Hyperbola. 
If a cone ABC (Fig. 10), of which A C is the base, 
is cut by a plane J K, parallel with but not through its 
axis, B G, and perpendicular to its base, the outline of 
the section thus obtained will be an open curve called a 
hyperbola, and shown by N J O (Fig. 11). 

If two cones (ABC and DBF, Fig. 10) are placed 
so that their apexes join, and if 
their axes, B G, B F, are in the 
same straight line, and they are 
cut by the same plane, H I L J K, 
parallel with F B G, the sec- 
tions thus obtained will form two 
hyperbolas, N J O and P I Q, as 
shown in Fig. 11, which are 
called the branches of the hy- 
perbola. I and J are the ver- 
tices of the curves, and the line I J, the distance be- 
tween the vertices, is the transverse axis. This is the 
same as I J in Fig. 10, and has been defined as that part 
of the axis which, if continued, 
would join an opposite cone. The 
conjugate axis, L M, is a line 
drawn through the transverse 
axis and at right angles to it. It 
is equal to twice the distance L B 
(Fig. 10), of the intersecting 
plane I J, from the axis of the 
Fig. II. cone from which the cone is pro- 




FiG. 10. 




duced. R R' (Fig. 11) are the foci of the two curves, 
and B, midway between I and J, is called the centre of 
the curve. The nature of the hyperbola is such that the 
difference of the distances of any point in the curve, 
from the foci, is always the same, and is equal to the 
transverse axis I J. Thus, if from the point i we draw 
lines I R and i R' to the foci R and R', then the 
difference of the length of these lines will be equal 
to I J. 

Plate 9. — Given the transverse and conjugate axes, 
to find the foci of an hyperbola: 

Let I J (Fig. 12) be the transverse axis of two 
branches of an hyperbola. The ends of the axis will 
coincide with the vertices of the two curves. From J 
erect J U, a perpendicular to I J, and make it equal to 
half the conjugate axis, or to the distance L B (Fig. 
10), of the intersecting plane from the axis of the cone. 
Then from B (Fig. 12), the middle of I J as a centre, 
and with B U as radius, describe the circle U R V R', 
cutting I J extended at R and R', which will be the foci 
of the hyperbola. 

The transverse and conjugate axes being given, to 
lay off an hyperbola: 

Draw I J (Fig. 12) equal to the transverse axis. 
Find the foci R R', as explained above. From R and R' 
lay off any number of points, i, 2, 3, etc., i', 2', 3', etc., 
at equal distances from R and R' respectively. Then 
with radii I i, I 2, I 3, etc., and from the foci as centres, 
describe arcs cutting each other at a, b, c, etc., and 



PLATE 9 




57 



S8 



A MANUAL OF MECHANICAL DRAWING. 



a! , V , c' , etc. These will give points in the curve 
through which it may be drawn. 

Fig. 13. — To drazv an hyperbola zvhen its length B C, 
its breadth D E, and transverse axis A B are given: 

Construct the parallelogram D E F G and subdivide 
its sides G D and E F and each of the ordinates, C D 
and C E, into the same number of equal parts, i, 2, 3, 
etc., and i', 2', 3', etc. From A draw lines to i, 2, 3, 
etc., and B draw lines to l', 2', 3', etc. ; where these lines 



cut those drawn from A to E D will be points through 
which the curve can be drawn. 

Plate 10. — The purpose of this plate is to show how 
the hyperbola is derived from the cone, and the method 
of procedure is exactly the same as explained in Plate 
8 for the parabola. All reference letters and figures 
and particular explanation are omitted, and the student 
is expected to develop the curve as indicated in the 
plate without the aid of explanations. 



PLATE 10 




60 



6o 



A MANUAL OF MECHANICAL DRAWING. 



Plate ii. The Parabola. 

Fig. 14. — The length A B and breadth C D being 
given, to draw a parabola: 

Draw A B to the given length and produce beyond 
A and B, draw C D perpendicular to A B through B, 
making C B and B D equal to half the given breadth. 
Bisect the ordinate C B and draw A E, and at right 
angles to A E draw E F. Make A G and A J each 
equal to B F. G is the focus of the parabola, and H I 
drawn through J is the directrix. Divide A B into 
spaces as 1,2, 3, etc., making spaces or intervals short- 
est near the vertex, and draw i, i', 2, 2', 3, 3', etc., 
perpendicular to A B. Take distance i J in compass, 
and with the focus as centre sweep arc cutting ordinate 
i-i' at i'. In like manner take distance of each ordinate 
from the directrix, and with focus as centre sweep arcs 
cutting the ordinates at 2', 3', 4', etc. These will be 
points in the curve which can be drawn through them. 



Fig. 15. — Length and breadth being given, to dra-w 
the parabola: 

Construct the parallelogram F E C D. Subdivide 
the ordinates B C and B D into any number of equal 
parts ; also divide F C and E D into a like number of 
equal parts. From A draw lines A i', A 2', A 3', etc., 
and from B D and B C draw from points i, 2, 3, etc., 
lines parallel with A B and cutting the lines drawn to 
i', 2', 3', etc. These will be points in the curve through 
which it may be drawn. 

Fig. 16. — Another method. Length A B and breadth 
C D being given. Produce A B, making A E equal 
to A B ; draw E C and E D, and draw 4' — 4 through A 
and parallel to C D. Divide E 4 and D 4 into the same 
number of equal parts, likewise E 4' and C 4', and draw 
lines 1-7', 2-6', 3-5', 5-3', etc. The curve will be 
tangent to these lines as shown. 



PLATE II 






61 



62 



A MANUAL OF MECHANICAL DRAWING. 



Plates 12 and 13. The Ellipse. 

If a cylinder or cone be cut by a plane at an angle 
to its axis, the outline of the curve obtained will be 
an Ellipse. 

In Plate 12 is shown a cylinder E F G H cut by the 
plane J K. To develop the ellipse : 

Draw the centre lines A B and C D perpendicular 
to each other, and with their point of intersection O 
as centre draw the circle CAD equal in diameter to 
the required cylinder, this will be the plan. Project 
the points C and D indefinitely to G and H. Draw 
G H perpendicular to A B, and measure G E the re- 
quired height of the cylinder. Draw E F parallel with 
G H, completing the elevation of the cylinder. Draw 
J K at any required angle to represent the cutting plane. 



With the 30°-6o° and 90° angles divide the circle 
CAD into equal parts, as at i, 2, 3, 4, and project 
these points upon the elevation, as at i-i', 2-2', etc. 
From points of intersection of J K and the lines i-i', 
2-2', etc., draw the indefinite lines a, b, c, d, etc., 
perpendicular to J K, and parallel with J K draw 
L M. With the intersection of lines g and L M as 
centre and radius equal to O C draw semi-circle i" 
M 4", and subdivide into equal parts as i", 2", 
M-3"-^", corresponding with points i, 2, 3, etc. 
From these points and parallel with L M draw lines, 
intersecting lines a, b, c, d, etc. These points of 
intersection will be points in the ellipse. 

The cone treated in the same way as above would 
likewise develop the ellipse. 



PLATE 12 







63 



64 



A MANUAL OF MECHANICAL DRAWING. 



Plate 13. — To draw an ellipse when the long and 
short diameters are given: 

Fig. 17. — Draw the concentric circles A B C D and 
E F G H equal, respectively, to the long and short 
diameters. Divide these circles into any number of 
equal parts, and draw diameters as I M, J N, etc. 
Where these diameters intersect the circles draw hori- 
zontal and vertical lines, as J 2, J' 2 and K 3, K' 3, etc. 
These points, 1-2-3-4, etc., will be points in the ellipse, 
which can be drawn through them. 

Fig. 18. — Another method. Draw rectangle whose 
sides, A D and B C, are equal to the long diameter, 
and A B and C D are equal to the short diameter of 
the required ellipse. Draw centre lines, F H and E G. 
Divide centre line F H into any number of equal parts, 
as O 3, 3-2, 2-1, etc. Also divide the short sides into 
the same number of equal parts, as A 3', 3'-2', 2'-i', 
etc. From G draw lines through points 1-2-3, ^tc, and 
from E draw lines to i', 2', 3', etc., and cutting the lines 
drawn from G. The intersections of these lines will 
give points in the curve. 



Fig. 19. — To drazv an ellipse whose axes are oblique: 
Construct the parallelogram whose sides are parallel 
with the axes, and proceed as with Fig. 18. 

The ellipses given on Plates 12 and 13 are true 
ellipses, such as would be developed from either a 
cylinder or cone cut by a plane. Many times an ap- 
proximate ellipse, which can be drawn directly by 
means of the compass, will meet all requirements. Four 
methods are given on Plate 14. 



Fig. 20. — The Oval. 

Draw centre lines A B and C D. With their inter- 
section O as centre describe a circle whose diameter is 
equal to the large end of the oval. From D draw D E 
and produce to F, likewise from C draw C E and pro- 
duce to G. With C as centre and radius C D draw the 
arc D G, and with D as centre and radius D C draw 
the arc C F. Then with E as centre and radius E F 
draw arc F B G, completing the oval. 



PLATE 13 



X-.. 




D r>& 20. 



66 



A MANUAL OF MECHANICAL DRAWING. 



Plate 14. Approximate Ellipses. 



To drazv an approximate ellipse with compass^ the 
major axis only being given: 

First Method. Fig. i. 

Draw A B equal to given length, divide into four 
equal parts A C, C D, D E and E B. With C and E 
for centres and radius C E draw intersecting arcs at 
F and G. From F and G through C and E draw in- 
definite lines G H, G I, F J and F K. 

With C and E as centres and radius C A draw arcs 
J A H and I B K, and with F and G as centres and 
radius G H draw arcs H I and J K. 

Second Method. Fig. 2. 

This is an ellipse of different proportion from those 
by the first method. 

Draw A B equal to the given length and divide into 
four equal parts, as A F, F E, E G and G B. Through 
E draw C D perpendicular to A B and make E H and 
E I equal to E F and E G. From H and I through 
F and G draw indefinite lines I K and I L and H J 
and H M. With F and G as centres and radius F A 
draw arcs K A J and L B M, and with I and H for 
centres and radius I K draw arcs K C L and J D M. 

Third Method. Fig. 3. 
To draw an approximate ellipse from four centres 
when both major and minor axes are given: 



Draw A B and C D perpendicular to and bisecting 
each other at O. Draw A E parallel with D C and 
E C parallel with A B. Bisect A E in F and draw 
F C. Draw E D cutting F C in G. With G and C as 
centres and any radius greater than half of C G draw 
intersecting arcs at H and I. From H through I draw 
line cutting C D at K. This line will be perpendicular 
to and will bisect G C. Draw G K cutting A B at M, 
and make O N equal to O M. Make O L equal to O K, 
and from I and K through M and N draw indefinite 
lines L P, L R and K O. With M and N as centres 
and radius M A draw arcs GAP and Q B R, and with 
centres at L and K and radius K G draw arcs G C Q 
and P D R. 

Fourth Method. Fig. 4. 

Giving different proportions from those by third 
method: 

Draw A B and C D perpendicular to and bisecting 
each other at O. Make O E equal to O C, and make 
O F and O G equal to A E. Draw F G and bisect at 
H. Make F I equal to F H. Make O K, O J and O L 
equal to O I. From K and L through I and J draw 
indefinite lines K O, K P, L M and L N. With I and J 
as centres and I A as radius draw arcs M A Q and 
N B P, and with K and L as centres and radius K Q 
draw arcs O D P and M N C. 



PLATE 14 



^ 




B A 




6 A 




F13.3.. 



Tij.^. 



68 



A MANUAL OF MECHANICAL DRAWING. 



CHAPTER VII. 



Various Curves. 



Plate 15. Spirals. 
Fig. 21. — To drazv an approximate spiral from two 
centres: 

Draw centre line A B, and on it mark the centres 

1 and 2, whose distance apart shall be equal to one-half 
the distance between the turns of the spiral. With i 
for centre and radius 1-2 sweep the semi-circle 2-3 ; 
then with 2 as centre and radius 2-3 sweep the semi- 
circle 3-4, and proceed in this way, using centres i and 

2 alternately. 

Fig. 22. — To draw an approximate spiral from three 
centres: 

Lay out an equilateral triangle whose sides are equal 
in length to one-third the distance between the turns of 
the spiral. Produce indefinitely the sides as i A, 2 B, 

3 C. With I as centre and 1-3 as radius draw the arc 
3-4, and with 2 as centre and 2-4 as radius draw the 
arc 4-5, and with 3 as centre and radius 3-5 draw arc 
5-6, etc. 

Fig. 23. — To draw an approximate spiral from four 
centres: 



Lay out a square whose sides will each be one-fourth 
the distance between the turns of the spiral, produce 
the sides as i-A, 2-B, 3-C, etc., and proceed as in previ- 
ous examples, using the angles as centres, but starting 
the spiral with radius equal to half the diagonal of the 
square, or the side of the square may be used as the 
first radius. 

Fig. 24. — To draw a true spiral: 

Draw a circle whose diameter is equal to the sweep 
of the spiral when revolved upon its centre, and divide 
it into as many equal parts as may be desired, and draw 
diameters 1-7, 2-8, 3-9, etc. Divide one semi-diameter 
or radius into as many equal parts as for the circle, as 
i'-2'-3'-4', etc. With compass in o and radius o-i' 
sweep an arc cutting radius i, with radius 0-2' sweep 
an arc cutting radius 2, with radius 0-3' sweep an arc 
cutting radius 3, and so on until all the points on the 
radius 12 have been used as radii for the arcs which 
cut the radii of the circumscribing circle. These inter- 
sections, a, h, c, d, etc., will be points through which the 
spiral can be drawn. 



PLATE 15 




r/G. 2/ 



//ID 




/3IB 



F,c. 23 




Fts. Z^ 



60 



70 



A MANUAL OF MECHANICAL DRAWING. 



In Plate i6 is given a practical application of the 
approximate spiral drawn from four centres. This 
drawing shows the case of a blower. The centres from 
which the outer curve is drawn are 4" apart, 2" each 
side of the centre line of the blower case. The cvtrve of 
the case ends at A, but is continued to B by the dotted 
line, to show that the distance between the turns of the 
spiral is just 4 times the distance between the centres 
from which they are drawn. 

The 3-centre spiral could be used for this same 
purpose, and is sometimes so used, but the resulting 



form of the case is not so well adapted to the purpose 
for which these blowers — that of moving air — are used. 
The same objection holds good with reference to the 
2-centre spiral. The draughtsman, however, finds 
numerous application's for all of these spirals in de- 
veloping odd curves that are required in his everyday 
work. 

In Fig. 27, Plate 17, is given a practical application 
of the true spiral in the development of the spiral or 
heart cam. 



PLATE i6 




71 



72 



A MANUAL OF MECHANICAL DRAWING. 



Plate 17. The Involute. 

Fig. 25. — If a string be wound around a circular 
block and a pencil be attached to the free end, the block 
being held to a plane surface, the pencil will, if held 
taut, and the string unwound, describe a curve called 
the involute of a circle, generally called the involute 
curve. 

About the centre A describe the required circle and 
divide it into any number of equal parts, o-i, 1-2, 2-3, 
etc. ; draw radii to these points, and to these radii draw 
tangents i-i', 2-2', 3-3', etc. Make one of these 
tangents 0-12 equal to the circumference of the circle 
A, and divide it into as many equal parts as was the 
circle. On tangent i-i' lay off one of these spaces, on 
tangent 2-2' two, on tangent 3-3' three, and so on until 
all of the tangents have been divided up or measured 
off, each succeeding tangent one space longer than the 
one preceding it. Through these points, i'-2'-3'-4' , etc., 
the curve may be drawn. 

Plate 18 is introduced to illustrate a practical ap- 
plication of the involute curve to laying out the single 
ctirve, or involute gearing. As will be seen, but a 
small portion of the curve is employed — the beginning 
of the curve. This is shown in the lower corner of the 
plate. 

In connection with the gear is shown a rack in 



"mesh." The rack is a straight gear, that is, the teeth, in- 
stead of being spaced around the periphery of a wheel, 
are equally spaced along a straight bar, and is employed 
to convert the rotary motion of the wheel into rec- 
tilinear motion, or the reverse. In the case of gear 
wheels the curve begins from an imaginary circle shown 
by dash and two dots, the other portion of the tooth 
being completed by radial lines. 

This plate is not introduced as a lesson in drawing 
gear teeth, but merely as an illustration of one of the 
applications of the involute curve in practice. 

Fig. 26. — To draw a three-centred cam: 

Lay off an equilateral triangle and continue the sides 
as shown, using the angles as centres from which to 
describe the curves of the cam, as follows : 

From A with radius A h describe the arc h d; from 
C with radius C d draw d f ; from B with radius B / 
draw / i; from A with radius A i draw i e ; from C with 
radius C e draw e g, and from B with radius B g draw 
g h. The centres A, B and C are not necessarily ar- 
ranged in the form of an equilateral triangle ; their po- 
sitions will be determined by the circumstances for 
which the cam is to be used. Such a cam has the 
property that any two parallel lines drawn tangent to it 
will always be the same distance apart. (See lines i'-2 
and 5-6; also 3-4 and 7-8.) 



PLATE 17 




F/G 2S 




Ffs.26 





!?< 


/' 




^ 


y 


« J 


f\( 






^ 


r\\ 


\ 5' 


i 


\v 






1 


) m 




<M 


1 


^ 


6 


2; . 

a . 

<< 


1 


/>-$ 



/y<r.27. 



73 



74 



A MANUAL OF MECHANICAL DRAWING. 



Plate 17, The Spiral Cam. 

Fig. 27 represents a cam whose outline is formed of 
two spirals. It possesses the property of imparting a 
uniform motion to a reciprocating piece of machinery. 

To lay out a spiral cam: 

Let ABC represent the hub of the cam and C D its 
stroke. Divide the circle A C B into a certain number 
of equal parts, say 12, and draw radial lines through 
the centre and extend them indefinitely. Next divide 
the stroke C D into half the number of equal parts, as 
in this instance 6, Nos. 1,2, 3, 4, etc. From the centre 
E with radius E i draw an arc cutting the radii i' and 
11'; from same Centre with radius E 2 draw an arc 



cutting the radial lines 2' and lo'; from E with radius 
E 3 draw an arc cutting the radial lines 3' and 9'. 
Continue this until all the radial lines have been marked 
off. Through the points thus measured the right and 
left curves may be drawn. The curve will begin at o 
and end at 6. Now suppose that the reciprocating part 
touches at o the beginning of the curve, it will have 
completed its stroke when the cam has made half a 
revolution, bringing the point 6 opposite the reciprocat- 
ing part or piece of the machine in which the cam is 
employed. From this it will be seen that the reciprocat- 
ing piece will make one-sixth of its stroke while the 
cam is moving through one-twelfth of its revolution. 



PLATE 1 8 




76 



A MANUAL OF MECHANICAL DRAWING. 



Plate 19. The Cycloid. 

The Cycloid is a curve which is described by any 
point in the circumference of wheel rolling on a straight 
line. 

In Fig. 28 let o-3'-6'-9' be a circle or wheel rolling on 
the straight line 0-12, equal in length to the circumfer- 
ence of the wheel. In rolling from o to 12 the point o 
in the circumference of the wheel will describe the 
curve a b c d, etc. The circle o, 3', 6', 9' is called the 
generating circle, and the point in the circle which 
describes the cycloid is the generator. The straight line 
on which the circle rolls is the director, and the line / 6 
is the axis of the cycloid. 

To lay off a cycloid for a wheel of any size: 

Draw the generating circle of the required diameter, 
next tangent to it draw the director o, 12, making it 
equal in length to the circumference of the generating 
circle. Draw o", 12" through the centre of the circle 
and parallel with 0-12. Divide the generating circle 
into an even number of equal parts, as o, i', 2', 3', etc. ; 
draw the chords o-ii', o-io', 0-9', 0-8' , 0-7' , 0-6' . Now 
divide the director into the same number of equal parts 
as is the generating circle, and draw the perpendiculars, 
i-i", 2-2", 3-3", etc. With i", 2", 3", etc., as centres 
and radius equal to radius of generating circle sweep 



arcs 1 a, 2 b, ^ c, etc., then with compasses set to length 
of chord o-ii' mark off points a and k from i and 11 ; 
likewise mark off b and / from 2 and 10, and so on until 
all the arcs have been measured off. These points, a b 
c d, etc., will be points in the cycloid. 

The Epicycloid (Fig. 29) is a curve which is de- 
scribed by any point in the circumference of a wheel 
which is rolling on the outside of a curved line. The 
process for laying out this curve is the same as for the 
cycloid, except that the lines which intersect the centre 
line of the generating circle, and giving the centres 
from which the arcs are drawn, are radial lines drawn 
from the same centre as the director, the line of centres 
being a curve concentric with the director. 

The arc of the director over which the generating 
circle rolls must be equal in length to the circumfer- 
ence of the generating circle. As it is somewhat diffi- 
cult to get this length correctly, an approximate method, 
as follows, may be employed : 

Divide the generating circle in equal parts, just as 
was done in the case of the cycloid; subdivide one of 
these parts into a number of small parts and space of¥ 
on the director the same number of these small sub- 
divisions. If this is carefully done the error is not ap- 
preciable. 



PLATE 19 




FiG.28 




It 



y8 A MANUAL OF MECHANICAL DRAWING, 



Plate 20. The Hypocycloid. The method of drawing this curve is the same as 

This is a curve which is described by any point in the that employed in drawing the epicycloid. A lengthy 

circumference of a wheel which is rolling on the inside description would only be a repetition of what has been 

of a curved line. said in regard to the cycloid and epicycloid. 



PLATE 20 




79 



8o 



A MANUAL OF MECHANICAL DRAWING. 



In Plate 21 is given an illustration of the application 
of the epicycloid and the hypocycloid to the drawing of 
cyclodial gear teeth. The generating circle is rolled on 
the outside and inside of the "director/^ which in this 
instance is the imaginary or pitch circle of the wheel. 
Only a small portion at the beginning of each curve is 
employed, as is clearly shown. In laying out a number 
of gear wheels which are to run together the same 
generating circle would be used for all of them, no 
matter how they may vary in size. Should different 



generating circles be employed the wheels would not 
fit each other, because the curve developed varies with 
the size of the generating circle. This can be proven 
by using two different generating circles for developing 
the curves and then fitting the curves together. 

In laying out a rack to work with a train of gears, the 
generating circles would be rolled on both sides of a 
straight line, thus developing the cycloid for both 
curves of the tooth — that is, above and below the pitch 
line. 



PLATE 21 




82 



A MANUAL OF MECHANICAL DRAWING. 



Plate 22. 
The Prolate Cycloid. — If the tracing point be within 
the circumference of the generating circle, the curve 
described by this point while the generating circle rolls 
on a straight line is called the prolate cycloid. This is 
the curve which is described by the centre of the crank 
pin of a locomotive when the driving wheel rolls upon 
the rails. The director is equal in length to the cir- 
cumference of the generating circle, and the sub- 
divisions are equal in number and length to those of 
the generating circle. The path of the generating point, 
if the wheel did not advance during its revolution, 
would be the small circle (Fig. 30), which is drawn 
inside the generating circle. It is subdivided to cor- 
respond with the subdivisions of the generating circle 
by radial lines drawn from the centre to the outer cir- 
cumference. The arcs and chords by which the points 
in the prolate cycloid are obtained are taken from the 
smaller circle, and are marked off exactly as for the 
cycloid, all of which is clearly given in Fig. 30. 



The Curtate Cycloid (Fig. 31) is a curve which is 
described by a tracing point which is without the gen- 
erating circle. 

The process of laying out this curve is clearly shown 
in Fig. 31, and is just the same as for the prolate 
cycloid (Fig. 30), except that the inner circle is the 
generating circle, while the outer one is the path of the 
tracing point if it did not advance during its revolution. 
In Fig. 30 another method of getting at the points in 
the curve is given. Instead of transferring the chords 
of the arcs by means of the compass, lines are drawn 
through the points in the circumference and parallel 
with the director. Where these lines intersect the 
arcs representing the generating circle drawn from 
the dividing points in the director, points will be 
found through which to draw the curve. This 
method may be employed for the cycloid and the 
prolate cycloid. In the case of the epicycloid and 
the hypocycloid, these lines would be drawn from 
the same centre as the director. 



PLATE 22 




Fy&. 3 O. 




/7<?. J/. 



83 



84 



A MANUAL OF MECHANICAL DRAWING. 



Plate 23. The Helix. 

Cut from a piece of thin paper, 
the right-angled triangle, CAB 
(Fig. 32), having its base or side, 
A B, ij inches long and the side, 
A C, 3.1416 inches long. If this 
triangle be wound around a 
cylinder one inch in diameter, with 
its side A B parallel with the axis 
G H of the cylinder (Fig. 33), the 
angle C will meet the angle A, and 
the hypothenuse will trace the line 
C D E F B, which line is called the 
helix. Or if the point C (Fig. 33) 
be moved at a uniform speed ij 
inches in a straight line, the 
cylinder at the same time 
making one revolution at a 
uniform rate of speed, the 
result of the two move- 
ments would be a line 
which would correspond 
exactly with the line 
traced by the hypothenuse of the triangle. The dis- 
tance A B which the point C moves during one revo- 




FiG. ;^2. 




lution of the cylinder is called the pitch, or lead, of the 
helix, and corresponds with the pitch of the ordinary 
screw-thread of a bolt. 

To draw a helix, the pitch and diameter being given: 

Draw the centre line E F (Fig. 34), draw semi- 
circle C F D equal in diameter to the required helix, 
draw C D and project C and D indefinitely parallel 
with E F. Divide semi-circle into any number of equal 
points, as i, 2, 3, 4, and project these points parallel 
with E F indefinitely. Lay off B D equal to the re- 
quired lead and divide into twice as many equal parts 
as used for the semi-circle, as i', 2', 3', 4', etc. ; pro- 
ject these points upon i, 2, 3, etc., produced as at a-b-c, 
etc. ; these intersections give points through which the 
helix may be drawn. In P'ig. 34 the pitch, or lead, is 
laid off on a line parallel with B D, but this is not 
necessary, as the subdivisions can be made upon either 
A C, B D or the centre line E F. 

To drazv a helical spring: 

Fig. 35. — Draw the helix as in Fig. 34, which would 
be the centre line of the spring. On this centre line 
draw small circles equal in diameter to the rod from 
which the spring is made, and draw lines tangent to 
these circles, as shown. The helix in Fig. 35 is finer 
than in Fig. 34. 



PLATE 23 





r/gss 



85 



^6 



A MANUAL OF MECHANICAL DRAWING. 



Plate 24. The Helix. 

To draw a V-thread screw: 

Draw centre line A B (Fig. 36), and on it draw 
semi-circle equal in diameter to the outside diameter of 
the screw. Subdivide and project the points, as in 
Fig. 32, lay off G H equal to pitch of thread, and sub- 
divide as before. With 30° angle draw E K and J K. 
Take distance K L in compasses, and with this for 
radius and O for centre draw circle MNP, which will 
be equal to the diameter at the bottom of the thread. 
Project the points from G H upon the lines drawn from 
points in the outer diameter of the screw and complete 
E Q of the helix. Now take G H in the dividers and 
point off on the lines from the outside diameter as 
many threads as are required ; having drawn lines of the 
helix through these points, with the 30° angle draw in 
the sides of the threads. In the same way project the 
points from the inner circle and draw in the curves of 
the helix representing the bottom of the thread. 

Fig. 35. — To drazt- a square-threaded screw: 

Draw circles representing the outside and inside 
diameters and draw the helix as A B, and on the lines 



projected from the circle which represents the diameter 
point off the thickness of the thread and the spaces 
between them, and through these points draw the curves 
of the helix, connecting the alternate curves by straight 
lines, as shown. Having completed the outer curves 
and the tops of the threads, draw the curves of lines 
representing the root or bottom of the thread. The 
square thread usually is made equal in depth to the face 
or width, and the space between the threads equal to 
the width. The thread may be considered as a square 
bar wound around a cylinder, the bar advancing as it is 
wound, so that the space between the coils will be equal 
to the width of the bar. The square thread is not al- 
ways of this proportion, being sometimes shallower ; 
also, the space may be either greater or less than the 
width of the thread, depending altogether upon the 
work to be done by it. 

The V or common thread may be considered as a 
triangular bar wound around a cylinder, but the edges 
of the bar are in contact. 

Both square and V threads are made either double or 
treble, etc., depending upon the speed of advance or 
lead required for each revolution. 



PLATE 24 




f/G37 



87 



88 



A MANUAL Oi" MECHANICAL DRAWING. 



CHAPTER VIII. 

Intersections and Envelopes. 



Plate 25. Intersection of Cylinder with Annidns. 

Draw centre lines A B, C D, and E F. With O as 
centre draw outside of annulus HEBE and inside 
I J K L, also circle shown in dash and two dots repre- 
senting centre of mass of annulus. Draw O G, and 
with Q its intersection with centre line of annulus as 
centre and Q G as radius draw circle equal in diam. to 
the cylinder. The centre of this circle may be placed 
at any point, depending upon the desired view. 

Project O indefinitely beyond C D and complete the 
outline of the cylinder M N P R; also complete the 



outline or side elevation of the annulus on centre 
line C D, as shown in the plate No. 25. 

Now take points I, 2, 3, 4, 5, 6, spaced at random, 
and with compasses from centre O transfer them to 
centre line E F, as i', 2', 3', etc. Project points 
i', 2', 3', etc., vertically across the side elevation of 
annulus, as i'", 2'", 3'", etc., and project these points 
of intersection across to i", 2", 3", etc. Now project 
points I, 2, 3, etc., vertically upwards to intersect with 
l", 2", 3", etc. These intersections will be points in the 
curved line which defines the intersection of the annulus 
and cylinder. 



PLATE 25 




so 



90 



A MANUAL OF MECHANICAL DRAWING. 



Plate 26. Intersection of Annuliis and Hexagonal 
Prism. 

The method for ascertaining the line of intersection 
in this case is exactly the same as for the previous 



lesson (Plate 25), and having- followed the several 
steps in that lesson, the student should have no 
difficulty whatever in doing Lesson 26. 

It is advisable that the student do both 25 and 26 
several times, varying the position of the centre Q. 



PLATE 26 




91 



92 



A MANUAL OF MECHANICAL DRAWING. 



Plate ■2'j. Intersection of Cone and Cylinder. 

Draw centre lines E F and G H. Complete outline of 
cylinder A B C D and draw semi-circle A E B. 

Draw outline of cone G J K, being sure that the 
cone is so located with reference to the cylinder that 
its diameter at the height E F is less than that of the 
cylinder. Produce A B to N and M. Produce J K 
to L. On the base of cone draw semi-circle J H K. 
Project G to H and make O L equal to half the 
diameter of base of cone. Draw N L and take points 
b and c at random, and through them draw Net 2"' 
and N f c i'", project points d, e, f to d' e' /', and 
a, h, c to a! V c' . With O for centre and l"' and 2"' 
and L for radii draw arcs 1"' , i" and 2"', 2" and L M, 



project i" across circle J H K to i, 4, and 2" to 2, 3 
and M to H ; project these points upon base of cone, as 
i', 2', 3', 4' , and from these points draw lines to vertex 
of cone. Where these lines intersect the lines drawn 
from a, h, c and d, e, f will be points in the curve de- 
fining the intersection. The plan of the intersection is 
found as follows : Draw a circle representing the 
cone in plan, on the centre line G H produce and draw 
upon it the plan of cylinder. Upon this circle project 
the points i, 2, 3, 4, and from them draw diameters. 
Upon these diameters project the points of intersection 
a', h', c' and d' , e' , f , and through these intersections 
draw the curves which complete the plan. These 
curves will form ellipses. 



PLATE 27 




t 




93 



94 



A MANUAL OF MECHANICAL DRAWING. 



Plate 28. Intersection of Two Cones. 

Draw in side elevation the two cones, being sure that 
the piercing cone shall be less in diameter than the 
one pierced at the point where their centre lines or axes 
cross. 

Produce the base C D indefinitely to N and M ; also 
produce base F G indefinitely to L and K. Draw K M, 
touching the vertices A and E of the cones A C D and 
E F G. Draw semi-circles on the bases of the cones, as 
F H G and C J D. Draw K N tangent to F H G, and 
from point of tangency 4 draw a line to the base F G 
and parallel with axis ; from point of intersection with 



base, draw a line to vertex E. Now take points i, 2, 3 
at random, and through them from vertex K draw 
lines to N C, cutting circle in i', 2', 3'. With O for 
centre transfer these lines to O L and on to the vertex 
M. Cutting the semi-circle C J D in points i", 2", 3", 
4" and i"', 2"', 3"',4"', project these points upon the base 
C D, and from them draw lines to vertex A. Now 
project points i, 2, 3 and i', 2', 3' upon base F G, and 
carry them on to vertex E. These lines will intersect 
those drawn from base C D in points which will be 
points in the curve of intersection. The plan of the 
intersections is drawn the same as that in Lesson 27, 




95 



96 



A MANUAL OF MECHANICAL DRAWING. 



Plate 29. Intersection of Cone and Sphere. 

With O at intersection of the centre Hnes, draw plan 
of the sphere. Draw O F at any required angle with 
centre line, and at some point as centre draw circle 
representing plan of cone. 

Project O and F indefinitely to A and C and parallel 
with each other. On centre line O A draw side eleva- 
tion of sphere, and on F C complete side elevation of 
cone C D E. Produce the base D E of the cone in- 
definitely to some point E'. Make D' E' equal to radius 
of cone base, and draw D' C ; project C to C, and draw 
C E'. This will represent half of the cone in elevation. 
Through the centre d of the sphere draw 4' d 4. and pro- 
duce indefinitely to the left. Make J K equal to O F, and 
with K for centre and radius equal to radius of sphere, 



sweep arcs cutting C E' at G" H". Project G" H" 
to G and H. Take any number of points on the 
sphere, as i, 2, 3, etc., and through them draw parallel 
with diameter 4, 4' the lines i-i', 2-2', 3-3', etc. 

With a I as radius sweep arcs in the plan with O for 
centre, as i-i ; then with a' i' as radius and F for centre 
sweep arcs cutting arcs i-i, project these points of 
intersection upon line a a' i' in the elevation. Proceed 
in the same way with b 2 and b' 2' and each of the 
others in succession, marking the points of intersection 
both in the plan and elevation until all the points in the 
curves are found. Now with F for centre and F' G" 
sweep arc intersecting O F at G', project G' to G. In 
the same way make F H' equal to F" H", and project 
H' to H. Through these points draw the curves which 
define the intersection both in elevation and plan. 



PLATE 29 




97 



9« 



A MANUAL UJ'" MECUANICAI, UKAWING. 



Plate 30. Intersection of Tivo Cylinders of Equal 
Diameter at Angle of 90°, and De- 
velopment of Envelope. 

Draw centre lines A B and C D at right angles, and 
with their intersection as centre draw circle ACE 
ecjual in diameter to the reqnired cylinders. l:'roject 
points A, C, O and P, as indicated in Plate 30, and 
draw G H and J K, completing side elevation of 
cylinders, with the exception of the line of inter- 
section. The two cylinders being of equal diameter, 
and placed at the angle of 90°, the line of intersection 
will be a straight line drawn from F to L. To demon- 
strate the correctness of this statement, divide the 
circle into any number of equal parts (twelve in this 
instan ce) , and through these poin t s d raw lines parallel 
with the centre lines. These lines will intersect in 
points which will be points in the line of intersection 
of the two cylinders. 



To lay out the flat sheets or envelopes which when 
rolled up into tubes would, when joined, form the right- 
angled elbow. Draw line M N and make it equal in 
length to the circumference of one of the cylinders. 
Divide into as many equal parts as was the circle ACE, 
and through these points, at i, 2, 3, etc., draw lines 
perpendicular to M N. Take distance i', 2' in com- 
passes and step or mark it off on each side of point 6, 
as 6, 2", 6-2"'. Next take i'-3' and step it off each 
side of point 6, as 6-3", 6-3"', and so on until all the 
points have been transferred to each side of point 6. 
Now transfer point 4"' to M and N, 3'" to i and 11, 2'" 
to 2 and 10. 6 to 3 and 9, 2" to 4 and 8, 3" to 5 and 7. 
A curve drawn through these points will be the de- 
veloped intersection of the cylinders. 

NoTL. — When the cylinders are of equal diameter 
the line of intersection will be a straight line, no matter 
what may be the angle at which the cylinders meet. 



PLATE 30 




LOFC 



00 



A MANUAL OF MECHANICAL DRAWING. 



Plate 31. To Lay Out an Elbow of Several Sections 
and to Develop a Section. 

Draw the right angle A O, O E. With O for centre 
and O A equal to the outer radius of elbow draw arc 
A B C D E, and from same centre and radius O F, 
equal to inner radius of elbow, draw arc F G H J K. 

Divide outer arc into as many equal parts as elbow is 
to have sections, and from centre O draw radial lines 
to the points of division, as B C D. Complete the 
straight sections A F N O and E K L M if they are 
required. This will complete the side elevation. 

To lay out one of the sections: 

On L M with centre O' draw semi-circle L R M and 
divide into equal parts, as 1,2, 3, 4. Parallel with E L 
draw I'-i, 2'-2, etc. With D and E for centres and 
radius greater than half of D E sweep intersecting arcs 



S, draw S O, parallel with D E draw line I'-i", 2'-2", 
etc. 

Draw a b and make it equal to circumference of pipe 
or elbow, or twice L R M, and divide it into twice as 
many equal parts as L R M, and draw lines at the 
points of division perpendicular to a b. 

Make lines at a and b each equal to J K, at i and 1 1 
each equal to 4'-4", and so on, finally m.aking 6 equal 
to D E. These should be taken from S O and laid off 
on each side of a b. Through the extremities of these 
lines curves are to be drawn, which will be the de- 
veloped lines of intersection of the sections. If the 
several sections are cut out of the sheet and rolled up 
and joined together they will form the elbow. In these 
exercises no allowance is made for laps for joining. 
The additional material for this purpose is added to one 
side and one end of the developed section, according to 
requirements of construction. 



PLATE 31 




102 



A MANUAL OF MECHANICAL DRAWING. 



Plate 2>^. Intersection of a Small Cylinder zvith a 
Large Cylinder at Angle of 30°. 

Draw elevation and plan, as shown in Plate 32. 

The drawing of the line of intersection is done ex- 
actly as in preceding lessons, and is clearly indicated in 
the plate. To develop the envelope of the small 
cylinder, draw g h and make it equal to the circumfer- 



ence of small cylinder and subdivide, as in previous 
lessons. Draw P R (see elevation) at right angles to 
axis of small cylinder. Transfer P 5' to ^ and h, e' 4' 
to J J' and t t', d' 3' to k k' and .y s', and so on until 
all the points have been measured off. Through these 
points, g j' k' I' in' , etc., draw the curve, which will be 
the developed line of intersection. 



PLATE 32 





I04 



A MANUAL OF MECHANICAL DRAWING. 



Plate 33. To Lay Out the Envelope of a Cone. 

Fig. 38. Draw cone ABC. With vertex A as 
centre and A C as radius draw arc C D, Make C D 
equal to circumference of base B C, and draw A D. 
To lay out the envelope of a hexagonal pyramid: 
Fig. 39. Draw semi-circle on base B C and divide 



into three equal parts, B i, 1-2, 2 C. Draw i-i', 2-2', 
and make A 3' equal to height of pyramid. Draw A B, 
A i', A 2', A C, completing side elevation of pyramid. 
With A for centre and radius A C draw indefinite arc, 
and on it step off C D, D E, E F, etc., each equal to 
1-2. Draw A D, A E, A F, etc., to complete the 
envelope. 



PLATE 33 




^ '' F.a%9 



K^ 2' C 



io6 



A MANUAL OF MECHANICAL DRAWING. 



Plate 34. To Drazv a Hemispherical Dome and to 
Develop in the Flat Sheet the Sections. 
Let C A D be the side elevation of the dome and 
E B F the plan. 

Divide the arc A C into any number of equal parts 
and draw lines through the points of division and 
parallel with the base C D, as 5'-i4', 6'-is' , etc. 

Divide the circumference in the plan into as many 
equal parts as there are to be sections in the dome, and 
draw diameters as at i, 2, 3, etc., and draw also in the 
plans circles equal in diameter to the sphere at 5'-i4', 
6'- 1 5', etc. Where these circles intersect the diameters 
are points, as i, 5, 6, etc., which are to be projected 
upon the lines in the elevation, as i', 5', 6', etc. These 
points, i', 2', 3', 4' and 5', 8', 11', 14', etc., are points 
through which curves are to be drawn representing the 
sections of the dome in elevation. 

To lay out one of the sections: 



Draw J K, making it equal to the arc A C, and divide 
it into the same number of equal parts as was the arc 
A C, and through the points of division draw a b, c d, 
e f, etc. Make a b equal to the arc 2, 3, c J equal to 
the arc 8, 11, and so on until all the lines are measured 
ofif, and through the extremities a, c, e, etc., draw 
curves to complete the figure, which will be the desired 
section of the dome. 

Another method : Make J K equal to the arc A C, 
and through K draw a b at right angles to J K, making 
a b equal to the arc 2, 3, and on it with K for centre 
draw semi-circle a j b, whose diamicter is equal to the 
length of arc 2, 3. Divide this semi-circle into as 
many equal parts as was the arc A C, and through the 
points of division draw lines parallel with a b, cutting 
the semi-circle in points a, c', c', etc., and project these 
points upon the lines c d, e f, g h. Through the points 
c e g ] and d f h J draw curves. 



PLATE 34 





io8 



A MANUAL OF MECHANICAL DRAWING. 



Plate 35. To Develop the Surface of a Square Prism 
with One of Its Corners Cut by a Plane at 45°. 
Begin by laying out adjacent rectangles to repre- 
sent the sides 1-2-3-4, adjoining a square representing 
the bottom and another the top. In the plan is shown 
the cutting plane a & in the envelope. Make a'-b' equal 
to a b. Make c'-d' equal to c d, and f'-g' equal to / g. 



Connect a'-b', c'-d' and f'-g'. Make d'-e' equal to 
d'-f, and f'-e' equal to a'-b'. 

To develop a hexagonal prism which is cut by a plane 
at an angle with its axis, follow the same method as 
given for the square prism, taking note that the 
hexagon to make the oblique face is elongated more or 
less, depending upon the angle of the face. 



PLATE 35 




\ 








(S / 






. 


V 






/ 




^ 


/ . 


N 


V 


«( 


o 


\ 


^ 


i 




» 






109 



A MANUAL Ul'' .MliClIANiCAL DRAWING. 



CHAPTER IX. 



Sections, Isometrical Projection and Shop Drawings. 



Plate 36. — A cube standing upon a corner, its bot- 
tom face at an angle of 45° with the horizontal, and cut 
by a vertical plane. To lay out the cube and develop 
the section : 

Fig. 40. — Draw A B with 45° angle, and at right 
angles to it draw B D and A G, making A B equal to 
the diagonal of the square side of the cube, and from 
its middle point E draw E F perpendicular to A B. 
Draw B D and A C parallel with E F. With E for 
centre and radius E B draw arc B G. As the figure 
is a cube, E B would be the radius of the circimiscribing 
circle, and the diagonal B G would equal the length of a 
side of the cube. Therefore with B as centre and B G 
as radius draw the arc G D, then B D will equal the 
length of a side of the cube. Draw D F C parallel with 
A B to complete the side elevation, and draw the per- 
pendicular O P for the cutting plane. Draw M N 
perpendicular, and upon it project the corners of points 
in the side elevation, and make K L and H J equal to 



A B, and complete the front elevation of the cube. 
Project the points in which O P cuts the side elevation 
upon the front elevation, and connect these points to 
complete the section, as shown by the shaded portion of 
the figure. 

Fig. 41. — Sections of an annulus. 

The side elevation shows half of the annulus, and 
the lines A B and C D are the cutting planes. The 
section at A B is clearly shown, and the student should 
be able to draw this section without any explanation. 
The same is to be said with reference to the section 
C D. Therefore the only particular explanation will 
be as to the method of determining the width of the 
section at E F. 

From centre O draw O L perpendicular to C D, and 
with L its intersection with the centre line of the 
annulus for centre and L 2 for radius draw the arc 
I, 2, 3. E F is the point 4 projected, and i, 4, 3 would 
be the width of the section at E F. 



PLATE 36 




/"/G -<'/ 



SCCTiJnC.D, 



A MANUAL OF MICCI r AN I CAT, DRAWING. 



Plate 37. — A sphere cut by a plane at an angle to its 
vertical axis. In the side elevation a straight line 
drawn to the required angle will represent the plane. 

The section in plan will take the form of an ellipse, 
and the method of developing this ellipse is clearly in- 
dicated. The elevation drawn perpendicular to the cut- 
ting plane would be a circle with diameter equal to the 
long diameter of the ellipse or the length of the chord 
which represents the cutting plane. 

A cylinder cut by two planes at different angles to 
the axis, said planes meeting at the centre of the 



cylinder. The end elevation shows the cutting plane, 
also the points which are to be projected upon the lines 
Or planes in the side elevation, and to be projected from 
the side elevation onto the plan. 

The plan shows points which are to be projected 
upon the pomts from the side elevation". The inter- 
sections of the projections from these points will give 
points in the- curves to complete the plan. A cylinder 
cut at an angle of 45° to its axis, when viewed in the 
plan, will show in the developed section a circle. 



PLATE 37 




114 



A MANUAL OF MECHANICAL DRAWING. 



ISOMETRICAL PROJECTION. 



Plate 38. — Objects drawn in isometrical show three 
of their faces in one view, all of which can be scaled or 
measured. 

It is a species of perspective, differing from linear 
perspective in that the lines are parallel instead of being 
drawn to meet in a "vanishing" point. 

Horizontal lines are drawn at an angle of 30° to the 
horizontal, which is equivalent to tipping the object 
upon one of its corners, if it is a rectangle or a solid, 
such as a rectangular prism, thus giving what might be 
called a "bird's-eye view." The principle of isometrical 
projection is shown in Fig. i, in which a rectangular 
prism is drawn in isometrical. The dimensions are, 
length i-|", breadth -J", height or thickness -J". By 
applying the scale to the figure it will be seen that all 
of these dimensions can be scaled off. The dotted 
regular hexagon is placed upon the figure to show that 
the lines are all drawn to the angles of 30° and 90° to 
the horizontal, so that the T square and the 30°-6o°-90° 
triangle are the principal tools required when working 
in isometrical. In Fig. 2 is shown a timber lying upon 
its side, with another timber having the same breadth 
and thickness standing upon one of its ends upon it. 

In Fig. 3 is shown a cube in isometrical, and standing 
upon the cube is a square pyramid, the base of the 
pyramid being smaller than the face of the cube. From 



this figure it will be seen that a regular hexagon gives 
the outline of the cube in isometrical. The dimensions 
are, for the cube, each face a f " square, base of pyramid 
a ^" square, height of pyramid I5". In drawing this 
figure, first draw a circle ij" diameter, and with 30° 
angle draw the four sides of the hexagon and the two 
radii, and with the 90° angle draw the vertical sides and 
the vertical radius. This will complete the cube.- Draw 
two diagonals on the upper face of the cube. Where 
they intersect will be the centre of the face, and from 
this centre measure the height of the pyramid. Lay 
out the base of pyramid by measuring the length of a 
side upon the side of the top face of the cube, as indi- 
cated by dotted lines. Draw lines parallel with the 
sides of the face of the cube, and where they intersect 
will be the corners of the base of the pyramid. From 
these corners draw lines to the vertex to complete the 
pyramid. 

Fig. 4 shows a simple truss. First draw the four 
outside members of the form and draw the diagon?.ls 
shown in dotted lines. These will be the centre lines 
of the diagonal braces. At the intersection of these 
centre lines draw a small circle whose diameter is equal 
to the face of the braces, and parallel with these centre 
lines and tangent to the circles draw the lines showing 
the thickness of the timber. Where the face line of the 



PLATE 38 




F/G./. 




Fjc.Z. 




ii6 



A MANUAL OF MECHANICAL DRAWING. 



diagonal intersects the vertical, draw a line across the 
face of the vertical, and where it intersects the other 
eds^e of the vertical will be the point which measures 
the width of the diagonal. From this point draw a line 
parallel with the face lines of the diagonal to define the 
top face. At the intersection of the diagonal draw a 
line across the top face of the diagonal, and where it 
intersects the back edge of the diagonal will be the 
point defining the width of the other brace. Through 
this point draw a line parallel with the front face to 
complete the second diagonal. 



In Fig. I, Plate 39, is shown a frame made up of' 
square timber. At each corner of the frame is a 
vertical timber smaller than that in the frame, the top 
ends of which are formed into tongues. The length 
and width of the frame would be measured along the 
lines A and B, the height or thickness of the timber 
on C, the breadth on D, while the distance the verticals 
are set back from the edge of the frame is measured off 
from the corner at E and F. Lines drawn from E and 
F parallel with A and B will intersect at the point from 
which the near corner of the vertical is to be drawn, 
while the two faces of the upright are measured from 
this near corner. In drawing this figure the pupil will 
work to the following dimensions, and use scale l" = 
I foot : 

Length of base (A), 8'-o" ; width of base (B), 6'-o". 



Tliickness of timber (C), 6"; width of timber 
(D).6". 

A'ertical timbers set back from edge (E and F), i". 

Width and thickness of verticals, 4". 

Height of verticals, 6'-o". 

Tennon in middle of timber, iV' thick, 3" long. 

In Fig. 2 is shown a box open at both ends, each face 
of which is a square. In the centre of the two front 
faces is a square hole. In the rear faces are also square 
holes, but these are not in the centre of the faces. 
Draw to the following dimensions : 

Faces of square sides of box, 2" square. 

Thickness of walls, \" . 

Openings in sides, i" square. 

Place openings in the centre of the two front or rear 
faces. In the rear faces the openings are i" below the 
top and -2" from the inside corner. Omit the shading. 

In Fig. 3 is shown a circle in isometrical. 

Two methods of drawing the circle are given. First 
method : Lay out the rhombus with major or long axis 
F G equal to diameter of the circle, bisect and draw 
perpendicular to it the minor or short axis. With 30° 
angle draw F B, G B, F A and G A. These lines will 
intersect at A and B, thus cutting off the correct length 
of the short axis. With centre O draw circles equal in 
diameter to F G and A B. Divide these circles and 
proceed as in lesson on Page 64, Plate 13, Fig. 17. 

Second method: Project A and B to either side. 
With C for centre, F G for radius, sweep an arc cut- 



PLATE 39 




117 



Il8 A MANUAL OF MECHANICAL DRAWING. 

ting A produced in D, draw C D and bisect in E and points of subdivision perpendicularly upon D C. With 

erect perpendicular. With E for centre and E C for O for centre and radius O G draw semi-circle and sub- 

radius draw semi-circle and subdivide, and project the divide, and proceed as in lesson on Page 52, Plate 7, 



PLATE 40 



ABCDE.rGH\JKLMNOPQRSTUVWXYZ 
abcdiefqh\jk\mnopqr5tuvwx^z 
1Z345 6 7 8 90 
AB CDEFGHIJKLMNOPQRSTUVWXYZ 
a be defqh ijklmnopq rstuvwxyz 
12345678 90 

AB CDEFGHIJKLMNOPQRSTUVWXYZ 

ABCDEFGHIJ K LM N O P Q R 5TU VWX Y Z 

1234567890 



120 



A MANUAL OF MECHANICAL DRAWING. 



Plate 41. Symbolical Shading. 

At one time the draughtsman represented the various 
materials by means of colors applied to the drawing 
with a brush. With the advent of the "blue printing" 
process it became necessary to abandon this method, 
owing to the fact that the colors would not print. Now 
colors are not used even for lines, and it is necessary 
to employ other means to convey to the workman the 
information in regard to the several metals or other 



materials to be employed. The line work shown on 
Plate 4t is now standard, and is employed by all work- 
shops of any- importance, and indeed by most of the 
smaller ones as well. When the shadings are not used 
the draughtsman must carefully mark each piece 
with the name of the material, and even when the 
symbolical shadings are used they can only be em- 
ployed for parts in section, therefore the name must 
be marked on full figures. This will be noted in the 
plates on shop drawing. 



PLATE 41 

Symbolical Shading. 




CAST IRON. 




WROUGHT IRON. 



•:$:$:*:*:*:J:$:J:$:*:J:*:^^ 









'///////////// '/^ '//////////////. 
'/////////'////'/"vz/y:"//-'/. 
y//ymy//////////////////////. 

V////////////////////////////A 

'y/////////////////////////////. 



COPPER. 







LEAD &. BABBITT. 




CONCRCTE. 



EARTH OR SAND. 



INDIA RUB6E.R. 



PLATE 42 




/Vg. 3. 



F,c. I. 




' I 




Fi&.^. 




F,G. 7. 
LINE SHADING. 



ria. Z.. 




122 



A MANUAL OF MECHANICAL DRAWING. 



Conventional Screw Threads. 



Screw threads are of many forms, those in most com- 
mon use being shown on Plate 43. 

The United States, or FrankHn Institute standard : 
The angle of the sides is 60°. The depth is -4- of the 
pitch, and the top and bottom are flattened an amount 
equal to one-eighth of the pitch. In the large work- 
shops of the United States this thread is standard, and 
it is used exclusively in all Government shops. 

Common, or V thread : Before the adoption of the 
United States standard thread this was the commonly 
used thread, and is still largely employed. The angle 
of the sides is 60°, 

The sc[uare thread is employed in machine tools and 
for many special purposes. It is especially valuable 
when a quick pitch is required, combined with great 
strength and comparatively large diameter at the bot- 
tom. That is, it is not as deep as either the U. S. or V 
threads would be with the same pitch. The proportions 
vary greatly, depending upon the service. The usual 
proportions, however, are as its name implies — square — 
the depth being equal to the width, which in turn is 
equal to half the pitch. 



The 15° thread is a modification of the square thread. 
Its sides have_ the "angle of 15°, its depth is equal to 
half the pitch, and its width at one-half its depth is half 
the pitch. Therefore to lay out this thread draw a 
pitch line half-way between the top and bottom of the 
thread, and on this line mark off the threads and spaces 
each equal to half the pitch. Through these points 
draw the sides of the thread at the angle of 15°. The 
sides will give the width of the thread at the top and 
bottom. This thread has all the advantages of the , 
square thread, with the added advantage of greater 
strength and slightly greater wearing surface for the 
same pitch. 

Any of these threads can be made right or left hand, 
double or treble, etc. 

The figures in this plate show the m.ethod usually 
emplo}'ed in the draughting room in drawing large 
screws, straight lines being employed to show* the 
threads, instead of the developed curves of the helix. 
This is done to economize in time. There are many 
occasions for drawing the true curves, therefore the 
draughtsman nmst be familiar with the method. 



PLATE 43 




us. STANDARD THREAD. 



COMMON 0/r' V THREAD 
.p. - 





5QUARE THREAD / 5" THREAD. 

CONVENTIONAL SCREW THREADS. 



124 



A MANUAL OF MECHANICAL DRAWING. 



Bolts and Nuts. 



On Plate 44 are shown a standard hexagon nut in 
Fig. I, a cap screw (Fig. 2), and a set screw (Fig. 3). 

To draw the standard nut or bolt head, take from the 
table on Page 128 the short diameter and draw a circle 
whose diameter is equal to the dimension given. Then 
with the 30°-6o° triangle and T square draw the sides 
of the nut tangent to this circle. The circle will repre- 
sent the chamfer of the nut or bolt head. Concentric 
with this circle draw in dotted line another circle equal 
in diameter to the bolt, and inside of this another circle 
equal to the diameter at the bottom of the thread. These 
two inner circles apply only to the nut. 

To draw the side elevation showing the short 
diameter, project i'-2'-3' either to the right or left, draw 
1-2-3 ^i^d parallel with it 4-5-6 spaced equal to the 
diameter of the bolt or the distance given in the table. 
With compass in 1-2 and 3 and radius 1-2 sweep in- 
tersecting arcs. With these intersections for centres 
and same radius draw the arcs 1-2 and 2-3. For the 
nut, project circles representing the thread. 

To draw elevation showing the long diameter, pro- 
ject the points 2' -2,'-^'-$" downward, and draw bottom 
and top of nut or bolt head as before. With radius 
equal to 3'-4" and centre on centre line of nut draw 
arc tangent to the top. Prolong this arc indefinitely 
across the other faces of the nut. Bisect 2'-3' and 



4'-5' in a and b, project a and h to a'-h'. These will 
be the centres of the small arcs which define the 
chamfer. If for nut, project the circles representing 
the thread. 

In Fig. 2 is shown a standard cap screiv. These are 
Unished tap bolts, having the heads smaller than the 
standard bolt heads. The top of the head is spherical 
in finish, and its height is equal to the diameter of the 
bolt. 

Dimensions of standard cap screw heads are given 
in the table on bolt heads and nuts. 

In Fig. 3 is shown a set screw. These are generally 
made with square heads, the short diameter of which is 
equal to the diameter of the bolt, the height of the head 
being of the same dimension. Under the head the bolt 
or body is reduced to the same diameter as the bottom 
of the thread. This is done to enable the thread to be 
cut all the way over the body. At the point there are 
several styles of finish, all of which are indicated, viz. : 
The cup, fiat and point. Sizes of standard set screw 
heads are given in the table, but if drawn with the 
short diameter and height equal to the diameter of the 
body of the screw they will be correct. 

The method of drawing the bolt head or nut as given 
above is correct for Unished nuts and heads, but it is 
rarely followed in the draughting room because of the 



PLATE 44 




oig2. 



STANDARD NUTS AND BOLTS. 



126 



A MANUAL OF MECHANICAL DRAWING. 



time consumed in a needless detail. The rule usually 
followed is to make the long diameter equal to twice 
the diameter of the bolt, and the height equal to the 
diameter of the bolt. The arcs showing the chamfer are 
drawn in by the eye, and the draughtsman soon be- 
comes expert at this. This makes the nut or bolt head 



larger in diameter than it is, in fact, and insures 
clearance. There are cases when it is necessary to draw 
to actual size, notably when clearances are small, and 
the student should be Samiliar with the method af 
doing it. 



128 



A MANUAL OF MECHANICAL DRAWING. 



% 

_5_ 
16 

v& 

7 



I 



2 
2K2 

3 

3^ 
3^ 

4 



20 
18 
16 
14 
13 
12 



7 
7 
6 
6 

5/2 

5 

5 

4'/^ 

4H 

4 

4 

3/3 

3/2 

3^ 

3 



SS 
so 

.185 
.240 
.294 

• 344 
.400 

• 454 

• 507 
.620 

• 731 

• 837 
.940 

1 . 065 
1. 160 
1.284 
1-389 
1.490 
i.6t5 
1. 712 
1.962 
2.175 
2.425 
2.628 
2.878 
3.100 
3-2^7 
3-566 



eg 

CO 






2-/8 



3/8 
3/3 
3% 

4H 

4V& 

5 

5M 

5^/4 

6K8 



TABLE VI. 
U. S. Standard Nuts, Bolt Heads and Threads 
•I I S 4K ' 



3«) 



% 



iV& 



HA 
III 

2A 

2/2 

2t?- 
2% 

3tV 



II 



1/2 



T6 
K2 



I^ 



5 

5J4 

5^ 

6 



23/^ 
25/^ 
2/2 
2'/ 
2% 



798 
027 
255 
480 
730 

953 
203 

423 



7H 



8H 



■zVa 

3tV 

3^ 

3lf 

4 

4t6 

4^ 

4X5 



Long diam. hexagon nut or bolt head = short diam. x 1.155. 

Long diam. square nut or boh head = short diam. x 1.414. 

Thickness of boh heads given in table is for rough heads. 

Thickness of finished heads and nuts is equal to diam. of 
bolt. Other dimensions given in table are finished sizes. 

Short diam. of rough nut or bolt heads = ij^ x diam. of 
bolt + Yi inch. 

In Plate 45 are given examples of conventional bolts 
and nuts, hexagon head and nut and square head and 
nut. When bolts of small size, and of any size to small 
scale, are drawn, the threads are represented as shown 
in the drawings, usually as in the upper one. The lines 
representing the top of the thread are fine, and extend 
at an angle entirely across the bolt, while those in- 
dicating the bottom of the thread are half-way between 
the tops of the thread, are heavy, and stop short of the 
sides. If left-hand thread is wanted it is so marked ; 
also if a special thread, double thread, triple thread or 
other departure from standard. No special instructions 
imply that the bolt is standu,-d. 



PLATE 45 





1 ' 


\ \ 


; 


\ \ /I 


. Jfe'. 


_ _ - _ > 



CONVENTIONAL BOLTS AND NUTS. 



130 A MANUAL OF MECHANICAL DRAWING. 



Shop Drawings. 

Plate 46 shows a common form of pillow block, or sions for making a drawing or pattern and for finishing 

bearing, for supporting shafting. It is shown in front are given. The student should practice upon this, 

and side elevations, and plan and all necessary dimen- making drawing to scale of ^ size, or 6" ^= 1 foot. 



PLATE 46 




PILLOW BLOCK. 



132 



A MANUAL OF MECHANICAL DRAWING. 



Plate 47 shows a flywheel with broad face, usually 
called a "band flywheel." 

The side elevation and section give all information 
required by pattern maker and machinist in making 
the wheel, and the student should proceed as follows 
in making the drawing : Draw first the horizontal and 
vertical centre lines for both views and then the circles 
for face or outer circumference, thickness of rim — 
dotted — and the inside flange, the bore of the hub and 
the outside of hub. There being six arms, draw centre 
lines of these arms. As the fillet or curve joining the 
arms to the rim is to be 3" radius, sweep arcs across 
the centre lines of the arms 3" from the dotted line. 
For thickness of arm on these arcs measure the width 
of the arm 5" or 2^" each side of the centre line. Next 
lay off the thickness of the arm at the hub 5f ", and the 
diameter 16" across the fillet connecting the arms at the 
hub. Draw in the sides of the arms, and with radius 
3" and centre on the arcs at the rim draw in the fillets 
tangent to the sides of the arms and the rim. Now 
find a radius by trial which will give an arc tangent 
to tw.o arms and the circle for fillet at the hub. 



Through the centre of this arc draw a circle concentric 
with the hub. On this circle will be found the centres 
for the arcs connecting the arms. 

The section shown is not a true section, in that the 
arm is not in section, but this method is usually em- 
ployed, as it saves making many views. Scale ofif each 
side of the centre line the v/idth of face, thickness of 
arm, length of hub and thickness of flanges, and draw 
the several lines parallel with the vertical centre line. 
Project the various diameters from the side elevation 
and draw in the fillets and keyway. 

The section of an arm can be drawn upon one of the 
arms, as shown, or it can be drawn elsewhere outside 
of the wheel to a large scale. The letter "f" shows 
where the wheel is to be machined. That is, the hub is 
to be bored and faced on both ends, and the outside is 
to be turned on the outside and "crowned," also is to 
be faced on both edges or sides. The directions 
"crowned"' ^", means that the rim is to be turned on 
the outside ^'^ higher in the middle than at the edges, 
the object of this crowning being to cause the band or 
belt to run fairly on the wheel. 



PLATE 47 




BAND FLY WHEEL. 



134 



A MANUAL OF MECHANICAL DRAWING. 



Plate 48 shows what is known as a "disc" crank for a 
steam engine, with crank pin and part of shaft. 

Draw first the vertical centre line and then the hori- 
zontal line for centre line of shaft, and parallel with it, 
and 12" apart, another centre line for the crank pin. 
On the centre line of the shaft draw the outside diam. 
of the crank, 43" or radius 21^", and inside of rim 41" 
diam. or 20J" radius; then diam. of hub 17" and shaft 
9^". Follow this by finishing the crank eye 5" 
radius and draw tangents for the crank ; then put in 
circles showing crank pin collar and crank pin, the lat- 
ter dotted, as it is behind the collar. With radius 5-|" 
sweep the arc showing where the projecting hub is cut 
away to level of crank face to clear for crank pin boxes 
and draw in the , key. The counterbalance is drawn 
from the rim tO' the hub 45° each side of the vertical 
centre line, and the lines of the counterbalance con- 
tinued would be tangent to the shaft, as shown by 
dotted lines. The section shows the rim 5" wide and 
the thickness through the hub 6", the hub projecting 



f " beyond the rim at the back and f " beyond the rim 
on the front. The web or plate is i^" thick, central 
with the rim, while the counterbalance is sunk ^" 
below the rim at the front, and projects f " at the back. 
The finishes are indicated by the letter /. 

The crank pin is shown in detail, drawn to a larger 
scale, and is partly in section. This section shows the 
cap to be a separate piece turned out to fit the projection 
on the end of the crank pin, and that it is held in place 
by a hollow bolt with a thick brass washer, having an 
oil groove turned inside which communicates with 
a pipe which is screwed into it. This pipe ex- 
tends to the centre of the shaft, terminating in a hollow 
ball through which the oil is fed to the pipe, the oil 
being thrown by centrifugal force through the pipe 
and hollow bolt and out of the oil hole which is bored 
from the side of the crank pin opposite the centre of the 
shaft. 

Make this drav/ing to scales 3" and 6" =^ i foot. 



PLATE 48 




DISC CRANK AND CRANK PIN. 



136 



A MANUAL OF MECHANICAL DRAWING. 



Plate 49 shows a solid crank shaft such as is used in 
the modern marine engine and in many vertical and 
horizontal land engines. Full dimensions and direc- 
tions for the shop are given. Also for the draughting 



room. Make a drawing to larger scale than the plate, 
say i" for the shaft and 3" for the coupling; also make 
detail of complete coupling or flange instead of half, as 
in the plate. 



PLATE 49 




■ieCT/Orr SHOtV/^C COl/fL'f^a BOJT. ' 

■■ I 



CRANK SHAFT fo» MARINE ENGINE 



138 



A MANUAL OF MECHANICAL DRAWING, 



Plate 50 shows driving wheel of a locomotive in 
front elevation and sections. Also sections giving the 
shape of the spokes at hub and rim. Directions for 
drawing the front elevation of the wheel, as well as the 
section, the same as given for Plate 45, while the details 



of the rim and tire are given on Plate 51. Make draw- 
ing to larger scale for elevation and section, say i" to 
the foot, while detail of the rim and tire may be drawn 
to scale of 3" = i foot. Note directions for finish, and 
be sure to give all necessary information on drawings. 



PLATE 50 




LOCOMOTIVE DRIVING WHEEL. 



PLATE 51 




SECTION OF RIM AND TIRE LOCOMOTIVE DRIVING WHEEL. 



I40 



A MANUAL OF MECHANICAL DRAWING. 



Plate 52. — A locomotive connecting rod. It will be 
noted that the ends only are shown, the body of the 
rod being "broken" away. Enough of the body is 
shown to indicate that it is tapered in width from 5" 
at the large end to 3f " at the small end, while the di- 
mension 8'-i^" from centre to centre (usually abbrevi- 
ated on drawing c to c) gives the necessary instruc- 
tions to the smith for making the forging. The gen- 
eral directions "steel forging, finished all over," 
shows that the smith is to allow for this finish by 
providing additional metal, and the machinist un- 
derstands that he is to machine and polish to every 



dimension. There being no sections to this drawing, 
none being necessary, the symbolical lines are not em- 
ployed to indicate the several metals employed, there- 
fore the names of these metals are marked on the pieces 
or parts. The boxes at the large end for the crank 
pin are of brass, lined in the bore with "babbitt" metal, 
which is retained in place by the "dovetails," while the 
small or "wrist pin" end is fitted with a brass liner 
or bushing, which is forced into place. 

Draw this to several scales, say i-|", 3" and 6" to the 
foot. 



PLATE 52 







®t-S=E3 



LOCOMOTIVE CONNECTING ROD. 



142 



A MANUAL OF MECHANICAL DRAWING. 



Plate 53. — Eccentric and strap for a marine engine. 
Only half of the strap is shown. Draw the eccentric 
and strap separate, making drawing of complete strap 
the other half of which is the same as the half shown. 

The eccentric is made in two parts, which are fitted 
with a tongue joint, the parts being held together by 
studs and keys. The eccentric has a "throw" of 4", 
which will impart a travel of 8" to the valve of the 
engine. First lay out the main centre lines — that is, 
those passing through the bore of the eccentric, and 4" 



from the centre of the bore and on the vertical centre 
line lay off the centre from Vyfhich the outside and in- 
side of rim are drawn to the radii given. Complete 
the details of the eccentric, both front elevation and 
section. The strap is in four pieces, the top and bottom 
straps and the two fillers. It is also lined with white 
metal or babbitt, which is held in place by the dovetails. 
Draw to scale of 3" = i foot for eccentric and strap, 
and 6" = i foot for details. 



PLATE 53 



£CC£//r/?/C A^o STRAP 




OE.TAIL SHOWING WHITE METAL LINING 



144 



A MANUAL OF MECHANICAL DRAWING. 



Exercises for Review. 



1 Draw plan of cube 2" on each face, standing at 
angle 30° and 60". Make front and side elevations. 

2 A rectangular prism i^" high, i^" wide, 3" long. 
An end elevation would show the prism resting upon 
one long edge, the sides at angles of 30° and 60° to the 
horizontal. Make plan and side elevation. Also oblique 
projection to show full view of one side. 

3 A cone with base 2" diameter, 3" high, pierces 
another cone having base 2^" diameter, ^^" high. The 
axis of the first cone is vertical, that of the pierced cone 
is at the angle of 60° with the axis of the first cone. 
Develop the lines of intersection. 

4 A hexagonal pyramid whose inscribed circle at 
the base is 2", and whose axis is 3", pierces a cone 
whose base is 2^" and height 3". The axes are at right 
angles, or 90° to each other. Develop the line of inter- 
section. 

5 A ring 3" inside diameter, 7" outside diameter, 
and whose section is a regular hexagon, is pierced by a 
cylinder i^" diameter. The axis of the cylinder is 
vertical to the plane of the ring, and is 4^' from the 
centre of the ring. A line connecting the centres of 
the ring and cylinder in plan is 30° to the horizontal 
centre line of the ring. Develop the lines of inter- 
section. 

6 A cone having base 2" diameter, axis 3" high, is 



revolved at a uniform velocity at the same time a point 
is moved along the side of the cone at the uniform 
velocity of i" for each revolution of the cone. De- 
velop the path of the point on the cone and make plan 
of the line traced. 

7 A hexagonal pyramid whose base is a regular 
hexagon circumscribed about a 2" circle, and whose 
height or length of axis is 3", is to be treated the same 
as was the cone in No. 6 above. 

8 An octagonal prism whose base is a regular 
octagon inscribed in a circle i^" diameter, and whose 
height on its axis is 2", cut by a plane at the angle of 
45°, the plane cutting the axis at its measured length 
of 2", thus making one face longer than the opposite 
face. Draw plan, front and side elevations, and find 
length of long and short sides. Also develop the en- 
velope. 

9 Draw in front and side elevation and plan a cross 
whose shaft is 6" square and 4' high, standing upon a 
base 6" thick and 2' square. The arms are 6" square 
and i' long each, and are i' below the top of shaft. 

10 Draw No. 9 in isometrical. 

11 Draw in isometrical a flight of six steps, whose 
dimensions are as follows : Length 6', width of tread 
12", height of riser 8". Each step is of one plank i^" 
thick, and is supported on three strings of 2" plank, 



A MA.NL'AI. Ol" MICCIIANICAL DUAW INT.. 



145 



those at the ends being set back 2" from the ends of 
the steps. The third string is in the middle of the steps. 

12 Draw in isometrical a truncated cone. Diameter 
of base 3", diameter of top lA", height 2". 

13 Draw a screw U. S. standard thread, 4" outside 
diameter, 3 threads per inch, 3" long, and make a sec- 
tion of a nut to correspond with it. Develop the curves 
of the helix. 

14 Draw- a square thread screws 4" outside diameter, 
i" pitch, left-hand thread, developing the true curves. 
Make section of nut to fit. 

Note. — In the section of a nut the thread is ap- 
parently the opposite hand to the thread of the screw. 



This is because in the elevation of the bolt the porti(jn 
of tlie tiiread in view is in front, whereas the nut being 
in section, the front portion is removed, leaving the 
rear in view. 

For further practice the pupil is advised to sketch 
odd pieces of machinery, or any objects that may be 
convenient, making careful measurements and mark- 
ing them on the sketches, and afterward making draw- 
ings from these sketches. By so doing he will gain 
valuable experience. Besides acquiring the habit of 
observing, he will also learn how to measure, what to 
take and what not to take, as well as how^ to represent 
the objects on his drawings. 



A \'i-:irriCAL Encinm-:, with Details ov Parts. 



In designing a piece of machinery, made up of a 
number of parts, the draughtsman first lays out a skele- 
ton drawing, on which he maps out the movements, 
both as to extent, direction, and the relation the move- 
ments bear to each other. After this is done he can 
take up the details — that is, the drawing of each sepa- 
rate part. 

Take as an example the vertical engine. The centre 
line of the shaft is first drawn, care being taken to so 
locate it that room will be left for the bed plate below 
it, and then the vertical centre lines for front and side 
elevations are drawn in. The next step will be to draw 



the centre line of the crank pin, which in the front or 
rear elevation would be a circle which projected upon 
the side elevation, or as in this case, section, would be 
two straight lines parallel with the centre line of the 
shaft, and showing the upper and lower positions of the 
crank pin corresponding to the extremes of travel of 
the piston. 

From the upper centre line, or top centre, the length 
of the connecting rod is measured upon the centre line 
which locates the "wrist pin,'' and from this the length 
of the crosshead, clearance between the crosshea<l and 
stuffing box, then the space or distance to the insiile face 



146 



A MANUAL OF MECHANICAL DRAWING. 



of C3-Iinder bottom. The next step is to lay out the clear- 
ance between cylinder bottom and the piston, thickness 
of piston, clearance between piston and top cylinder head, 
with the stroke of piston added. This gives the neces- 
sary inside length of the cylinder, and the cylinder is 
then drawn in, with the heads, walls and valve chest. At 
this point the position of the centre line of the valve 
stem is determined with reference to the centre line of 
the cylinder. The main dimensions and form of the 
bed plate and framing, together with the location and 
sizes of shaft bearings, guides, etc., are determined 
and drawn in for reference in detailing. Finally the 
guide for the valve stem is located and outlined as to 
form, and the position of the eccentric on the main shaft 
located. The draughtsman now takes up the matter of 
detailing, and his first step in this direction is to design 
the cylinder, with its steam and exhaust ports, the valve 
chest, valve, cylinder heads, and all the parts that go to 
make up the cylinder complete. 

This is usually followed by the bed plates and frames 
on "housings," after which come the other details, until 
all the parts are drawn completely, and dimensions and 
full instructions for the shop embodied therein. In 
making the details, those parts that are to be made of 
cast iron or cast steel are grouped or kept together, 
and forgings are kept separate from them, the reason 



for this being that the pattern maker who makes the 
patterns from which the moulder produces the castings 
has nothing whatever to do with the smith's work, 
which is confined to the forgings, nor has the smith 
any business with the castings. The brass parts are 
kept, as far as possible, in a group or class, but the 
drawings for them go to the pattern maker. 

Having completed all the details, the draughtsman 
takes his skeleton drawing in hand again and puts all 
the details into this drawing, thus assembling the parts 
and making the "general'' drawing, or "assembly" 
drawing. In working out the details it may be neces- 
sary to alter the dimensions from those allotted to some 
of the parts, and it will therefore be necessary to alter 
the general drawing to correspond. As each drawing 
or sheet of drawings is completed it is checked at every 
point by another draughtsman, who places his initials 
upon it. 

In making a set of drawings of the engine, which 
are included among the "shop" drawings, the pupil is 
expected to work as described above. Further, he 
should work entirely by the dimensions given, and not 
to transfer from the plates, by scale or otherwise, as his 
work will not come out right, the plates having been 
photographed off scale. 



PLATE 54 




PLATE 55 




•DETAILS 8" X 6" VERTICAL ENGINE. 




DETAILS 8' X 6" 
VERTICAL ENGINE. 




CKl//\fOS/? N£AO. OAfe- CASr //POf/-. 



PLATE 59 




PfSTO/Y ONE i:A5T/RON 
^/SrOA/ f?OD, ONE, 5T££L 









LOCK NUT roff PISTOr^ ROD . 

O^V£ STCEL FINISh ALL OVCR. 



DETAILS 8" X 6" VERTICAL ENGINE. 



PLATE 60 




V3_^ 



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DETAILS 8' X 6' VERTICAL ENGINE, 



PLATE 6i 
















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PLATE 62 




DETAILS 8" X 6" VERTICAL ENGINE. 



PLATE 63 





PLATE 64 




BOXES fOK MAIf/ BeARIUG5. TiA/O. B/?ASS. 








MAI/^ BEARING CAP. TWO. 5Te£L 



DETAILS 8" X 6" VERTICAL ENGINE. 



o/L CUP eoy£R. 

TWO. CAST l/fO/V. 



PLATE 65 





PLATE 66 







NUTS FINISHE.0 
CASE HARDNEO. 



CRANK END BOLT- TWO - ST££L FlNtSHE-O. 



DETAILS 8" X 6" VERTICAL ENGINE. 



PLATE 67 




DETAILS 8" X 6" VERTICAL ENGINE. 



PLATE 68 




C/fOSS h£/>^0, 0/V£ cast t/jOAT , 
^'/^/3/Y£0 ALL OVER. 




CROSS HCAO KE.LPER, S,r££i. _ 
ONe^ ^//V/5H£0 ALL Ove'R. 




f/LL£R fOR 6/8, rv\^0, 



C^/3 BOLT Tv^o 5T££l, 



DETAILS 8" X 6" VERTICAL ENGINE. 



PLATE 69 





•^M 



:..-)£-- 






- _2i J 

ORli'lNG FIT IN Gun 



~NtcO" 



E.NO RIVtLTED OvCIR 
AND FINISHED FL03H. 



,<, ^.8_ ^ 

valve: 5T£M GUIDE PIN 

ONE STEtL /"/VLL OVER. 



/^ 



DETAILS 8' X 6" VERTICAL ENGINE. 



INDEX. 



PAGE. 

Annulus and Cylinder 88 

Annulus and Hexagonal Prism 9" 

Annulus, Sections of no 

Block, Diflferential 27 

Bolts, Conventional 128 

Board, Drawing 15 

Bows, Spring 12, 21 

Care of Instruments 12 

Cam, Spiral 74 

Cam, Three-cornered 72 

Cap Screws 128 

Circle, The 24 

Compass 10, 13. 21 

Compass, Beam 2j 

Connecting Rod 140 

Crank, Disc 134 

Crank Shaft 136 

Cylinder, Projections of 52 

Cycloid 76 

Cycloid, Prolate 82 

Cycloid, Curtate 82 

Curves, French or Irregular 22 

Definitions, Geometrical 2 

Dimensions 16, 20 



14Y 



PAGE. 

Disc Crank 134 

Dividers 13. 21 

Decimal Equivalents, Inches 29 

Decimal Equivalents, Feet 30 

Drawing Pen 12, 2 j 

Driving Wheel 138 

Dome, Spherical 106 

Eccentric and Strap 138 

Ellipse 62, 64 

Ellipse, Approximate 66 

Elbow, Square 98 

Elbow in Several Sections 100 

Envelope of Cone 104 

Envelope of Hexagonal Pyramid 104 

Envelope of Dome 106 

Envelope of Square Elbow 98 

Envelope of Elbow in Several Sections 100 

Envelope of Hexagonal Prism 108 

Envelope of Cube ; 108 

Envelope of Cylinder 98, 102 

Engine, Vertical 145 

Epicycloid 70 

Exercises for Review 144 

Fly Wheel 13.' 

Finish Marks i() 

Figuring Solidity and Weights 37 



148 



INDEX. 



PAGE. 

Hexagonal Prism 48, 108 

Hexagonal Prism, Intersecting Annulus 90 

Helix 84 

Helical Spring 84 

Hypocycloid 78 

Hyperbola 56, 58 

Inclined Plane 27 

Involute 73 

Intersection Annulus and Cylinder 88 

Intersection Annulus and Hexagonal Prism 90 

Intersection Cylinder and Cone 92 

Intersection, Two Cones 94 

Intersection Cone and Sphere 96 

Intersection Two Cylinders 98, 102 

Isometrical Projection 114-124 

Keyways, Standard ^ 39 

Lines 16 

Lines, Shade 17 

Line Shading 18 

Lettering 18 

Levers 26 

Mensuration Surfaces and Solids 24 

Mechanical Powers 26 

Nuts, Standard , 124 

Nuts, Conventional 128 

Oval 64 

Parabola 54. 60 

Paper, Mounting on Board 15 

Pens, Drawing 12. 22 



PAGE. 

Pencils, Drawing 15, 22 

Pillow Block 130 

Planes, Inclined 27 

Problems, Geometrical 6 

Protractor 22 

Projection, Planes of 40 

Projection, Prism and Cube 42 

Projection, Triangular Prism 44 

Proj ection of Cube 46 

Projection, Hexagonal Prism 48 

Projection, Cylinder 52 

Projection, Hexagonal Pyramid 50 

Pulley, The 27 

Scales 20, 22 

Screw, The 28 

Screw Threads, Conventional 122 

Screws, Cap and Set 124 

Section Lining 17 

Section of Cube no 

Section of Annulus no 

Selection of Instruments 10 

Section of Cylinder 112 

Section of Sphere 112 

Shading. Line 18 

Shading, Symbolical 120 

Sketching 20 

Square, T 22 

Standard Keyways 39 

Spirals 68 

Spiral Cam 74 

Symbols 24 

Table, Decimal Parts of Inch 29 

Table, Decimal Parts of Foot 30 



INDEX. 



149 



PAGE. 

Tabic, Areas and Circumferences of Circles 31 

Table. Tensile Strength of Materials 38 

Table, Weight of Substances, Cubic Foot 38 

Table, Weight of Substances, Cubic Inch 38 

Table, Standard Key ways 39 

Table, Bolts and Nuts 12S 

Table, Cap and Set Screws 128 

Tangents, How to Draw 21 

Titles 19 

Triangles 1 5, 22 

Triangular Frisni, Projections 44 

Use of Instruments 14 

Vertical Engine 145 

■Wedge, The 28 

Wheel. Fly 132 

Wheel, Locomotive Driving 138 

Plates of Verticai. Encine and Details. 

PLATE. 

Bed Plate 57 

Bushing, \'al vc 60 

Cylinder 55 

Cylinder Head 58 



PLATE. 

Crank Shaft 61 

Connecting Rod 61 

Crank Shaft Boxes 64 

Crank Pin 66 

Crank End Bolts, etc 66 

Cross Head and Details 68 

Eccentric Rod 69 

Eccentric and Strap 67 

Eccentric Rod End 67 

Frame, Upright 56 

General Drawing 54 

Main Bearing Caps 64 

Main Bearing Bolts, Nuts and Keeper 65 

Oil Cup Cover 64 

Piston and Rings 39 

Piston Rod and Nut 59 

Piston Valve 60 

Valve, Piston 60 

Valve, Bushing 60 

Valve. Chest Cover Top 58 

Valve. Che.st Cover Bottom and Details 62 

V'alve, Stem Gland and Nut 62 

Valve, Stem Guide Bracket 63 

Valve, Stem Guide Pin and Cap 69 

Valve, Stem Guide 67 

Valve, Stem 69 



APR 13 1907 



i;-»?rJ?;!»trfH5,'i;J5Sc 



mm 

LIBRARY OF CONGRESS^ fj 



019 970 510 6 












